Question 1

Calculate the Riemann Sum for the integral using $n = 4$ .   $\int _ { 0 } ^ { 10 } e ^ { - x ^ { 2 } } d x$ 
 
Round to the nearest tenth.

Accepted Answer

A)  1.1 
B)   1 
C)   1.3 
D)   2.1 
E)  2.5 
A)  1.1 
B)   1 
C)   1.3 
D)   2.1 
E)  2.5

Question 2

Calculate the total area of the region bounded by the line $y = 17 x$ , the x-axis, and the lines $x = 3$ and $x = 5$ . Round your answer to the nearest whole number.

Accepted Answer

A) 272 
B)  833 
C)  136 
D)  34 
E)  17 
A) 272 
B)  833 
C)  136 
D)  34 
E)  17

Question 3

Evaluate the integral.  $\int _ { 5 } ^ { 9 } \left( \frac { 46 } { x ^ { 2 } } + 101 x \right) \mathrm { d } x$

Accepted Answer

A)  $\left( \frac { 46 } { 9 } - \frac { 46 } { 5 } \right) + 50.5 \left( 9 ^ { 2 } - 5 ^ { 2 } \right)$ 
B)  $\left( \frac { 46 } { 9 } - \frac { 46 } { 5 } \right) + 101 \left( 9 ^ { 2 } - 5 ^ { 2 } \right)$ 
C)  $\left( \frac { 46 } { 5 } - \frac { 46 } { 9 } \right) - 101 \left( 9 ^ { 2 } - 5 ^ { 2 } \right)$ 
D)  $\left( \frac { 46 } { 5 } - \frac { 46 } { 9 } \right) + 50.5 \left( 9 ^ { 2 } - 5 ^ { 2 } \right)$ 
E)  $\left( \frac { 46 } { 5 } - \frac { 46 } { 9 } \right) + 50.5 ( 9 - 5 )$ 
A)  $\left( \frac { 46 } { 9 } - \frac { 46 } { 5 } \right) + 50.5 \left( 9 ^ { 2 } - 5 ^ { 2 } \right)$ 
B)  $\left( \frac { 46 } { 9 } - \frac { 46 } { 5 } \right) + 101 \left( 9 ^ { 2 } - 5 ^ { 2 } \right)$ 
C)  $\left( \frac { 46 } { 5 } - \frac { 46 } { 9 } \right) - 101 \left( 9 ^ { 2 } - 5 ^ { 2 } \right)$ 
D)  $\left( \frac { 46 } { 5 } - \frac { 46 } { 9 } \right) + 50.5 \left( 9 ^ { 2 } - 5 ^ { 2 } \right)$ 
E)  $\left( \frac { 46 } { 5 } - \frac { 46 } { 9 } \right) + 50.5 ( 9 - 5 )$

Question 4

Evaluate the integral.   $\int \frac { x + 3 } { x ^ { 4 } } d x$

Accepted Answer

A)  $- \frac { 1 } { 3 x ^ { 2 } } - \frac { 1 } { x ^ { 2 } } + C$ 
B)  $- \frac { 1 } { 2 x ^ { 2 } } - \frac { 1 } { x ^ { 3 } } + C$ 
C)  $- \frac { 1 } { 2 x ^ { 2 } } + \frac { 1 } { x ^ { 3 } } + C$ 
D)  $\frac { 1 } { 2 x ^ { 2 } } + \frac { 1 } { x ^ { 3 } } + C$ 
E)  $\frac { 1 } { 2 x ^ { 2 } } - \frac { 1 } { x ^ { 3 } } + C$ 
A)  $- \frac { 1 } { 3 x ^ { 2 } } - \frac { 1 } { x ^ { 2 } } + C$ 
B)  $- \frac { 1 } { 2 x ^ { 2 } } - \frac { 1 } { x ^ { 3 } } + C$ 
C)  $- \frac { 1 } { 2 x ^ { 2 } } + \frac { 1 } { x ^ { 3 } } + C$ 
D)  $\frac { 1 } { 2 x ^ { 2 } } + \frac { 1 } { x ^ { 3 } } + C$ 
E)  $\frac { 1 } { 2 x ^ { 2 } } - \frac { 1 } { x ^ { 3 } } + C$

Question 5

Evaluate the integral.   $\int \left( 6 x ^ { 23 } - x ^ { - 6 } + 2 \right) d x$

Accepted Answer

A)  $\frac { x ^ { 23 } } { 4 } + \frac { x ^ { - 7 } } { 7 } + 2 x + C$ 
B)  $\frac { x ^ { 24 } } { 4 } - \frac { x ^ { - 5 } } { 5 } + 2 x + C$ 
C)  $\frac { x ^ { 24 } } { 4 } + \frac { x ^ { - 5 } } { 5 } + 2 x$ 
D)  $\frac { x ^ { 24 } } { 4 } + \frac { x ^ { - 5 } } { 5 } + 2 x + C$ 
E)  $\frac { x ^ { 24 } } { 4 } + \frac { x ^ { - 5 } } { 5 } + C$ 
A)  $\frac { x ^ { 23 } } { 4 } + \frac { x ^ { - 7 } } { 7 } + 2 x + C$ 
B)  $\frac { x ^ { 24 } } { 4 } - \frac { x ^ { - 5 } } { 5 } + 2 x + C$ 
C)  $\frac { x ^ { 24 } } { 4 } + \frac { x ^ { - 5 } } { 5 } + 2 x$ 
D)  $\frac { x ^ { 24 } } { 4 } + \frac { x ^ { - 5 } } { 5 } + 2 x + C$ 
E)  $\frac { x ^ { 24 } } { 4 } + \frac { x ^ { - 5 } } { 5 } + C$

Question 6

Your name is Francesca Dragonetti (an assistant of Galileo Galilei) and, to impress your boss, you toss a weight upward at 32 feet per second from the top of the Leaning Tower of Pisa (height 185 ft). Neglecting air resistance, find the weight's velocity and the height of the weight above the ground as a functions of time in seconds. ?

Accepted Answer

A)  $v ( t ) = 10 t$ , $s ( t ) = 185 + 32 t - 5 t ^ { 2 }$ 
B)  $v ( t ) = 32 + 32 t$ , $s ( t ) = 185 + 32 t + 16 t ^ { 2 }$ 
C)  $v ( t ) = 32 - 32 t$ , $s ( t ) = 32 t - 16 t ^ { 2 }$ 
D)  $v ( t ) = 32 - 32 t$ , $s ( t ) = 185 + 32 t - 16 t ^ { 2 }$ 
E)  $v ( t ) = 32 t$ , $s ( t ) = 32 t - 16 t ^ { 2 }$ 
A)  $v ( t ) = 10 t$ , $s ( t ) = 185 + 32 t - 5 t ^ { 2 }$ 
B)  $v ( t ) = 32 + 32 t$ , $s ( t ) = 185 + 32 t + 16 t ^ { 2 }$ 
C)  $v ( t ) = 32 - 32 t$ , $s ( t ) = 32 t - 16 t ^ { 2 }$ 
D)  $v ( t ) = 32 - 32 t$ , $s ( t ) = 185 + 32 t - 16 t ^ { 2 }$ 
E)  $v ( t ) = 32 t$ , $s ( t ) = 32 t - 16 t ^ { 2 }$

Question 7

The marginal cost of producing the xth roll of film is given by $7 + \frac { 9 } { ( x + 2 ) ^ { 2 } }$ .  
The total cost to produce one roll is $700. Find the total cost function $C ( x )$ .

Accepted Answer

A)   $C ( x ) = 7 x + \frac { 9 } { x + 2 } + 696$ 
B)    $C ( x ) = 7 x - \frac { 9 } { x + 2 } + C$ 
C)   $C ( x ) = 7 x + \frac { 9 } { x + 2 }$ 
D)   $C ( x ) = 7 x - \frac { 9 } { x + 2 } + 696$ 
E)    $C ( x ) = 7 x - \frac { 9 } { x + 2 }$ 
A)   $C ( x ) = 7 x + \frac { 9 } { x + 2 } + 696$ 
B)    $C ( x ) = 7 x - \frac { 9 } { x + 2 } + C$ 
C)   $C ( x ) = 7 x + \frac { 9 } { x + 2 }$ 
D)   $C ( x ) = 7 x - \frac { 9 } { x + 2 } + 696$ 
E)    $C ( x ) = 7 x - \frac { 9 } { x + 2 }$

Question 8

Evaluate the integral.   $\int _ { 8 } ^ { 12 } \left( 12 x - 69 x ^ { 0.2 } \right) \mathrm { d } x$

Accepted Answer

A)  $12 \left( \frac { 8 ^ { 2 } } { 2 } - \frac { 12 ^ { 2 } } { 2 } \right) - 69 \left( \frac { 12 ^ { 0.2 } } { 0.2 } - \frac { 8 ^ { 0.2 } } { 0.2 } \right)$ 
B)  $12 \left( \frac { 12 ^ { 3 } } { 3 } - \frac { 8 ^ { 3 } } { 3 } \right) - 69 \left( \frac { 8 ^ { 1.2 } } { 1.2 } - \frac { 12 ^ { 1.2 } } { 1.2 } \right)$ 
C)  $12 \left( \frac { 12 ^ { 2 } } { 2 } - \frac { 8 ^ { 2 } } { 2 } \right) + 69 \left( \frac { 12 ^ { 1.2 } } { 1.2 } - \frac { 8 ^ { 1.2 } } { 1.2 } \right)$ 
D)  $12 \left( \frac { 12 ^ { 2 } } { 2 } - \frac { 8 ^ { 2 } } { 2 } \right) - 69 \left( \frac { 12 ^ { 1.2 } } { 1.2 } - \frac { 8 ^ { 1.2 } } { 1.2 } \right)$ 
E)  $12 \left( \frac { 12 ^ { 2 } } { 2 } - \frac { 8 ^ { 2 } } { 2 } \right) + 69 \left( \frac { 12 ^ { 1.2 } } { 1.2 } + \frac { 8 ^ { 1.2 } } { 1.2 } \right)$ 
A)  $12 \left( \frac { 8 ^ { 2 } } { 2 } - \frac { 12 ^ { 2 } } { 2 } \right) - 69 \left( \frac { 12 ^ { 0.2 } } { 0.2 } - \frac { 8 ^ { 0.2 } } { 0.2 } \right)$ 
B)  $12 \left( \frac { 12 ^ { 3 } } { 3 } - \frac { 8 ^ { 3 } } { 3 } \right) - 69 \left( \frac { 8 ^ { 1.2 } } { 1.2 } - \frac { 12 ^ { 1.2 } } { 1.2 } \right)$ 
C)  $12 \left( \frac { 12 ^ { 2 } } { 2 } - \frac { 8 ^ { 2 } } { 2 } \right) + 69 \left( \frac { 12 ^ { 1.2 } } { 1.2 } - \frac { 8 ^ { 1.2 } } { 1.2 } \right)$ 
D)  $12 \left( \frac { 12 ^ { 2 } } { 2 } - \frac { 8 ^ { 2 } } { 2 } \right) - 69 \left( \frac { 12 ^ { 1.2 } } { 1.2 } - \frac { 8 ^ { 1.2 } } { 1.2 } \right)$ 
E)  $12 \left( \frac { 12 ^ { 2 } } { 2 } - \frac { 8 ^ { 2 } } { 2 } \right) + 69 \left( \frac { 12 ^ { 1.2 } } { 1.2 } + \frac { 8 ^ { 1.2 } } { 1.2 } \right)$

Question 9

Evaluate the integral.  $\int \left( ( 6 x - 1 ) e ^ { 6 x ^ { 2 } - 2 x } + 5 x e ^ { x ^ { 2 } } \right) \mathrm { d } x$

Accepted Answer

A)   $\frac { e ^ { 6 x ^ { 2 } - 2 x } + 5 x e ^ { x ^ { 2 } } } { 2 x } + C$ 
B)   $\frac { e ^ { 6 x ^ { 2 } - 2 x } + 5 e ^ { x ^ { 2 } } } { 2 } + C$ 
C)   $e ^ { 6 x ^ { 2 } - 2 x } + 10 e ^ { x ^ { 2 } } + C$ 
D)   $e ^ { 6 x ^ { 2 } - 2 x } + 5 e ^ { x ^ { 2 } } + C$ 
E)    $\frac { e ^ { 6 x ^ { 2 } - 2 x } + 5 e ^ { x ^ { 2 } } } { x } + C$ 
A)   $\frac { e ^ { 6 x ^ { 2 } - 2 x } + 5 x e ^ { x ^ { 2 } } } { 2 x } + C$ 
B)   $\frac { e ^ { 6 x ^ { 2 } - 2 x } + 5 e ^ { x ^ { 2 } } } { 2 } + C$ 
C)   $e ^ { 6 x ^ { 2 } - 2 x } + 10 e ^ { x ^ { 2 } } + C$ 
D)   $e ^ { 6 x ^ { 2 } - 2 x } + 5 e ^ { x ^ { 2 } } + C$ 
E)    $\frac { e ^ { 6 x ^ { 2 } - 2 x } + 5 e ^ { x ^ { 2 } } } { x } + C$

Question 10

Evaluate the given integral using the substitution.  
  $\int e ^ { - 4 x } \mathrm {~d} x ; u = - 4 x$

Accepted Answer

A)  $- e ^ { - 4 x } + C$ 
B)    $- 4 e ^ { - 4 x } + C$ 
C)    $- \frac { 1 } { 4 } e ^ { - 4 x } + C$ 
D)    $- \frac { 1 } { 4 } e ^ { - 8 x } + C$ 
E)    $- e ^ { - 8 x } + C$ 
A)  $- e ^ { - 4 x } + C$ 
B)    $- 4 e ^ { - 4 x } + C$ 
C)    $- \frac { 1 } { 4 } e ^ { - 4 x } + C$ 
D)    $- \frac { 1 } { 4 } e ^ { - 8 x } + C$ 
E)    $- e ^ { - 8 x } + C$

Question 11

Find $f ( x )$ if $f ( 0 ) = 0$ and the tangent line at $( x , f ( x ) )$ has the slope $x \left( x ^ { 2 } + 2 \right) ^ { 3 }$ .

Accepted Answer

A)  $\frac { x ^ { 2 } + 2 } { 8 } + C$ 
B)   $\frac { x ^ { 2 } + 2 } { 8 }$ 
C)   $\frac { \left( x ^ { 2 } + 2 \right) ^ { 4 } } { 4 } + 4$ 
D)   $\frac { \left( x ^ { 2 } + 2 \right) ^ { 4 } } { 8 } - 2$ 
E)    $\frac { \left( x ^ { 2 } + 2 \right) ^ { 4 } } { 4 } - 4$ 
A)  $\frac { x ^ { 2 } + 2 } { 8 } + C$ 
B)   $\frac { x ^ { 2 } + 2 } { 8 }$ 
C)   $\frac { \left( x ^ { 2 } + 2 \right) ^ { 4 } } { 4 } + 4$ 
D)   $\frac { \left( x ^ { 2 } + 2 \right) ^ { 4 } } { 8 } - 2$ 
E)    $\frac { \left( x ^ { 2 } + 2 \right) ^ { 4 } } { 4 } - 4$

Question 12

Evaluate the integral.   $\int 2 x \sqrt { 4 x ^ { 2 } - 4 } d x$

Accepted Answer

A)   $\frac { \sqrt { \left( 4 x ^ { 2 } - 4 \right) } } { 2 } + C$ 
B)  $\frac { \left( 4 x ^ { 2 } - 4 \right) \sqrt { 4 x ^ { 2 } - 4 } } { 4 } + C$ 
C)    $\frac { \left( 4 x ^ { 2 } - 4 \right) \sqrt { 4 x ^ { 2 } - 4 } } { 6 } + C$ 
D)     $\frac { \left( 4 x ^ { 2 } - 4 \right) \sqrt { 4 x ^ { 2 } - 4 } } { 2 } + C$ 
E)    $\frac { \left( 4 x ^ { 2 } - 4 \right) \sqrt { 4 x ^ { 2 } - 4 } } { 12 } + C$ 
A)   $\frac { \sqrt { \left( 4 x ^ { 2 } - 4 \right) } } { 2 } + C$ 
B)  $\frac { \left( 4 x ^ { 2 } - 4 \right) \sqrt { 4 x ^ { 2 } - 4 } } { 4 } + C$ 
C)    $\frac { \left( 4 x ^ { 2 } - 4 \right) \sqrt { 4 x ^ { 2 } - 4 } } { 6 } + C$ 
D)     $\frac { \left( 4 x ^ { 2 } - 4 \right) \sqrt { 4 x ^ { 2 } - 4 } } { 2 } + C$ 
E)    $\frac { \left( 4 x ^ { 2 } - 4 \right) \sqrt { 4 x ^ { 2 } - 4 } } { 12 } + C$

Question 13

Calculate the Riemann Sum for the integral using n = 10. 
$\int _ { 3 } ^ { 4 } 3 x e ^ { 1.7 x } d x$  
Round the answer to four decimal places.

Accepted Answer

A) 4,257.7370 
B)  5,335.1538 
C)  5,261.3439 
D)  5,187.5341 
E)  42,577.3704 
A) 4,257.7370 
B)  5,335.1538 
C)  5,261.3439 
D)  5,187.5341 
E)  42,577.3704

Question 14

The marginal cost function for the manufacture of portable CD players is given by 
$C ^ { \prime } = 50 - \frac { x } { 500 }$ 
where  x is the number of CD players manufactured. Use a Riemann sum with n = 5 to estimate the cost of producing the first 5 CD players. Round your answer to the nearest cent.

Accepted Answer

A) $249.96 
B)  $249.95 
C)  $224.98 
D)  $249.97 
E)  $249.98 
A) $249.96 
B)  $249.95 
C)  $224.98 
D)  $249.97 
E)  $249.98

Question 15

Evaluate the integral.   $\int _ { 7 } ^ { 15 } \left( x ^ { 3 } - 43 x \right) \mathrm { d } x$

Accepted Answer

A) 8,272 
B)  88 
C)  12,056 
D)  20,328 
E)  3,792 
A) 8,272 
B)  88 
C)  12,056 
D)  20,328 
E)  3,792

Question 16

Evaluate the integral.   $\int x e ^ { - 4 x ^ { 2 } + 1 } \mathrm {~d} x$

Accepted Answer

A)  $- 8 e ^ { 4 x ^ { 2 } + 1 } + C$ 
B)    $- \frac { e ^ { - 4 x ^ { 2 } + 1 } } { 8 } + C$ 
C)    $- \frac { e ^ { 4 x ^ { 2 } + 1 } } { 4 } + C$ 
D)    $- e ^ { 4 x ^ { 2 } + 1 } + C$ 
E)    $- \frac { x e ^ { 4 x ^ { 2 } + 1 } } { 8 } + C$ 
A)  $- 8 e ^ { 4 x ^ { 2 } + 1 } + C$ 
B)    $- \frac { e ^ { - 4 x ^ { 2 } + 1 } } { 8 } + C$ 
C)    $- \frac { e ^ { 4 x ^ { 2 } + 1 } } { 4 } + C$ 
D)    $- e ^ { 4 x ^ { 2 } + 1 } + C$ 
E)    $- \frac { x e ^ { 4 x ^ { 2 } + 1 } } { 8 } + C$

Question 17

Evaluate the integral mentally.  $\int ( - 5 ) d x$

Accepted Answer

A)  $5 x + c$ 
B)  $5 x$ 
C)  0 
D)  $- 5 x$ 
E)  $- 5 x + c$ 
A)  $5 x + c$ 
B)  $5 x$ 
C)  0 
D)  $- 5 x$ 
E)  $- 5 x + c$

Question 18

Use the given graph to estimate the left Riemann sum for the given interval with the stated number of subdivisions.  $[ 0,3 ] ; n = 3$

Accepted Answer

A) Left Sum = 1 
B)  Left Sum = 2 
C)  Left Sum = - 2 
D)  Left Sum = 0 
E)  Left Sum = - 1 
A) Left Sum = 1 
B)  Left Sum = 2 
C)  Left Sum = - 2 
D)  Left Sum = 0 
E)  Left Sum = - 1

Question 19

Find $f ( x )$ if $f ( 8 ) = 24$ and the tangent line at $( x , f ( x ) )$ has slope x. ?

Accepted Answer

A)  $f ( x ) = \frac { x ^ { 2 } } { 2 } - 8$ 
B)  $f ( x ) = \frac { x ^ { 2 } } { 2 } - C$ 
C)  $f ( x ) = - \frac { x ^ { 2 } } { 2 } + 8$ 
D)  $f ( x ) = \frac { x ^ { 2 } } { 2 } + C$ 
E)  $f ( x ) = \frac { x ^ { 2 } } { 2 } + 8$ 
A)  $f ( x ) = \frac { x ^ { 2 } } { 2 } - 8$ 
B)  $f ( x ) = \frac { x ^ { 2 } } { 2 } - C$ 
C)  $f ( x ) = - \frac { x ^ { 2 } } { 2 } + 8$ 
D)  $f ( x ) = \frac { x ^ { 2 } } { 2 } + C$ 
E)  $f ( x ) = \frac { x ^ { 2 } } { 2 } + 8$

Question 20

Calculate the Riemann Sum for the integral using n = 4.  
 $\int _ { 1 } ^ { 5 } x ^ { 2 } d x$

Accepted Answer

A) 16 
B)  24 
C)  30 
D)  54 
E)  26 
A) 16 
B)  24 
C)  30 
D)  54 
E)  26

Calculate the Riemann Sum for the integral using $n = 4$ . $\int _ { 0 } ^ { 10 } e ^ { - x ^ { 2 } } d x$ Round to the nearest tenth.

Calculate the total area of the region bounded by the line $y = 17 x$ , the x-axis, and the lines $x = 3$ and $x = 5$ . Round your answer to the nearest whole number.

Evaluate the integral. $\int _ { 5 } ^ { 9 } \left( \frac { 46 } { x ^ { 2 } } + 101 x \right) \mathrm { d } x$

Evaluate the integral. $\int \frac { x + 3 } { x ^ { 4 } } d x$

Evaluate the integral. $\int \left( 6 x ^ { 23 } - x ^ { - 6 } + 2 \right) d x$

The marginal cost of producing the xth roll of film is given by $7 + \frac { 9 } { ( x + 2 ) ^ { 2 } }$ . The total cost to produce one roll is $700. Find the total cost function $C ( x )$ .

Evaluate the integral. $\int _ { 8 } ^ { 12 } \left( 12 x - 69 x ^ { 0.2 } \right) \mathrm { d } x$

Evaluate the integral. $\int \left( ( 6 x - 1 ) e ^ { 6 x ^ { 2 } - 2 x } + 5 x e ^ { x ^ { 2 } } \right) \mathrm { d } x$

Evaluate the given integral using the substitution. $\int e ^ { - 4 x } \mathrm {~d} x ; u = - 4 x$

Find $f ( x )$ if $f ( 0 ) = 0$ and the tangent line at $( x , f ( x ) )$ has the slope $x \left( x ^ { 2 } + 2 \right) ^ { 3 }$ .

Evaluate the integral. $\int 2 x \sqrt { 4 x ^ { 2 } - 4 } d x$

Calculate the Riemann Sum for the integral using n = 10. $\int _ { 3 } ^ { 4 } 3 x e ^ { 1.7 x } d x$ Round the answer to four decimal places.

Evaluate the integral. $\int _ { 7 } ^ { 15 } \left( x ^ { 3 } - 43 x \right) \mathrm { d } x$

Evaluate the integral. $\int x e ^ { - 4 x ^ { 2 } + 1 } \mathrm {~d} x$

Evaluate the integral mentally. $\int ( - 5 ) d x$

Use the given graph to estimate the left Riemann sum for the given interval with the stated number of subdivisions. $[ 0,3 ] ; n = 3$

Find $f ( x )$ if $f ( 8 ) = 24$ and the tangent line at $( x , f ( x ) )$ has slope x. ?

Calculate the Riemann Sum for the integral using n = 4. $\int _ { 1 } ^ { 5 } x ^ { 2 } d x$

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Exam 13: The Integral

Calculate the Riemann Sum for the integral using n=4n = 4n=4 . ∫010e−x2dx\int _ { 0 } ^ { 10 } e ^ { - x ^ { 2 } } d x∫010​e−x2dx Round to the nearest tenth.

Calculate the total area of the region bounded by the line y=17xy = 17 xy=17x , the x-axis, and the lines x=3x = 3x=3 and x=5x = 5x=5 . Round your answer to the nearest whole number.

Evaluate the integral. ∫59(46x2+101x)dx\int _ { 5 } ^ { 9 } \left( \frac { 46 } { x ^ { 2 } } + 101 x \right) \mathrm { d } x∫59​(x246​+101x)dx

Evaluate the integral. ∫x+3x4dx\int \frac { x + 3 } { x ^ { 4 } } d x∫x4x+3​dx

Evaluate the integral. ∫(6x23−x−6+2)dx\int \left( 6 x ^ { 23 } - x ^ { - 6 } + 2 \right) d x∫(6x23−x−6+2)dx

The marginal cost of producing the xth roll of film is given by 7+9(x+2)27 + \frac { 9 } { ( x + 2 ) ^ { 2 } }7+(x+2)29​ . The total cost to produce one roll is $700. Find the total cost function C(x)C ( x )C(x) .

Evaluate the integral. ∫812(12x−69x0.2)dx\int _ { 8 } ^ { 12 } \left( 12 x - 69 x ^ { 0.2 } \right) \mathrm { d } x∫812​(12x−69x0.2)dx

Evaluate the integral. ∫((6x−1)e6x2−2x+5xex2)dx\int \left( ( 6 x - 1 ) e ^ { 6 x ^ { 2 } - 2 x } + 5 x e ^ { x ^ { 2 } } \right) \mathrm { d } x∫((6x−1)e6x2−2x+5xex2)dx

Evaluate the given integral using the substitution. ∫e−4x dx;u=−4x\int e ^ { - 4 x } \mathrm {~d} x ; u = - 4 x∫e−4x dx;u=−4x

Find f(x)f ( x )f(x) if f(0)=0f ( 0 ) = 0f(0)=0 and the tangent line at (x,f(x))( x , f ( x ) )(x,f(x)) has the slope x(x2+2)3x \left( x ^ { 2 } + 2 \right) ^ { 3 }x(x2+2)3 .

Evaluate the integral. ∫2x4x2−4dx\int 2 x \sqrt { 4 x ^ { 2 } - 4 } d x∫2x4x2−4​dx

Calculate the Riemann Sum for the integral using n = 10. ∫343xe1.7xdx\int _ { 3 } ^ { 4 } 3 x e ^ { 1.7 x } d x∫34​3xe1.7xdx Round the answer to four decimal places.

Evaluate the integral. ∫715(x3−43x)dx\int _ { 7 } ^ { 15 } \left( x ^ { 3 } - 43 x \right) \mathrm { d } x∫715​(x3−43x)dx

Evaluate the integral. ∫xe−4x2+1 dx\int x e ^ { - 4 x ^ { 2 } + 1 } \mathrm {~d} x∫xe−4x2+1 dx

Evaluate the integral mentally. ∫(−5)dx\int ( - 5 ) d x∫(−5)dx

Use the given graph to estimate the left Riemann sum for the given interval with the stated number of subdivisions. [0,3];n=3[ 0,3 ] ; n = 3[0,3];n=3

Find f(x)f ( x )f(x) if f(8)=24f ( 8 ) = 24f(8)=24 and the tangent line at (x,f(x))( x , f ( x ) )(x,f(x)) has slope x. ?

Calculate the Riemann Sum for the integral using n = 4. ∫15x2dx\int _ { 1 } ^ { 5 } x ^ { 2 } d x∫15​x2dx

Functions and Applications

Nonlinear Functions and Models

The Mathematics of Finance

Systems of Linear Equations and Matrices

Matrix Algebra and Applications

Linear Programming

Sets and Counting

Probability

Random Variables and Statistics

Introduction to the Derivative

Techniques of Differentiation

Applications of the Derivative

Further Integration Techniques and Applications of the Integral

Functions of Several Variables

Trigonometric Models

Filters

Calculate the Riemann Sum for the integral using $n = 4$ . $\int _ { 0 } ^ { 10 } e ^ { - x ^ { 2 } } d x$ Round to the nearest tenth.

Calculate the total area of the region bounded by the line $y = 17 x$ , the x-axis, and the lines $x = 3$ and $x = 5$ . Round your answer to the nearest whole number.

Evaluate the integral. $\int _ { 5 } ^ { 9 } \left( \frac { 46 } { x ^ { 2 } } + 101 x \right) \mathrm { d } x$

Evaluate the integral. $\int \frac { x + 3 } { x ^ { 4 } } d x$

Evaluate the integral. $\int \left( 6 x ^ { 23 } - x ^ { - 6 } + 2 \right) d x$

The marginal cost of producing the xth roll of film is given by $7 + \frac { 9 } { ( x + 2 ) ^ { 2 } }$ . The total cost to produce one roll is $700. Find the total cost function $C ( x )$ .

Evaluate the integral. $\int _ { 8 } ^ { 12 } \left( 12 x - 69 x ^ { 0.2 } \right) \mathrm { d } x$

Evaluate the integral. $\int \left( ( 6 x - 1 ) e ^ { 6 x ^ { 2 } - 2 x } + 5 x e ^ { x ^ { 2 } } \right) \mathrm { d } x$

Evaluate the given integral using the substitution. $\int e ^ { - 4 x } \mathrm {~d} x ; u = - 4 x$

Find $f ( x )$ if $f ( 0 ) = 0$ and the tangent line at $( x , f ( x ) )$ has the slope $x \left( x ^ { 2 } + 2 \right) ^ { 3 }$ .

Evaluate the integral. $\int 2 x \sqrt { 4 x ^ { 2 } - 4 } d x$

Calculate the Riemann Sum for the integral using n = 10. $\int _ { 3 } ^ { 4 } 3 x e ^ { 1.7 x } d x$ Round the answer to four decimal places.

Evaluate the integral. $\int _ { 7 } ^ { 15 } \left( x ^ { 3 } - 43 x \right) \mathrm { d } x$

Evaluate the integral. $\int x e ^ { - 4 x ^ { 2 } + 1 } \mathrm {~d} x$

Evaluate the integral mentally. $\int ( - 5 ) d x$

Use the given graph to estimate the left Riemann sum for the given interval with the stated number of subdivisions. $[ 0,3 ] ; n = 3$

Find $f ( x )$ if $f ( 8 ) = 24$ and the tangent line at $( x , f ( x ) )$ has slope x. ?

Calculate the Riemann Sum for the integral using n = 4. $\int _ { 1 } ^ { 5 } x ^ { 2 } d x$