Question 1

Evaluate the integral.   $\int \left( \frac { 4 } { x ^ { 0.2 } } - \frac { 5 } { x ^ { 1.1 } } \right) d x$

Accepted Answer

A)  $\frac { x ^ { - 1.2 } } { 0.2 } + \frac { 50 } { x ^ { 2.1 } } + C$ 
B)  $\frac { x ^ { - 1.2 } } { 0.2 } + \frac { 50 } { x ^ { 2.1 } }$ 
C)  $\frac { x ^ { 0.8 } } { 0.2 } - \frac { 50 } { x ^ { 0.1 } } + C$ 
D)  $\frac { x ^ { 0.8 } } { 0.2 } + \frac { 50 } { x ^ { 0.1 } } + C$ 
E)  $\frac { x ^ { 0.8 } } { 0.2 } + \frac { 50 } { x ^ { 0.1 } }$ 
A)  $\frac { x ^ { - 1.2 } } { 0.2 } + \frac { 50 } { x ^ { 2.1 } } + C$ 
B)  $\frac { x ^ { - 1.2 } } { 0.2 } + \frac { 50 } { x ^ { 2.1 } }$ 
C)  $\frac { x ^ { 0.8 } } { 0.2 } - \frac { 50 } { x ^ { 0.1 } } + C$ 
D)  $\frac { x ^ { 0.8 } } { 0.2 } + \frac { 50 } { x ^ { 0.1 } } + C$ 
E)  $\frac { x ^ { 0.8 } } { 0.2 } + \frac { 50 } { x ^ { 0.1 } }$

Question 2

A race car has a velocity of $v ( t ) = 600 \left( 1 - e ^ { - 1.6 t } \right) \frac { \mathrm { ft } } { \mathrm { s } }$ , t seconds after starting. Use a Riemann sum with n = 10 to estimate how far the car travels in the first 2 seconds. (Round your answer to the nearest whole number.)

Accepted Answer

A) 780 feet 
B)  713 feet 
C)  895 feet 
D)  576 feet 
E)  846 feet 
A) 780 feet 
B)  713 feet 
C)  895 feet 
D)  576 feet 
E)  846 feet

Question 3

The oxygen consumption of a bird embryo increases from the time the egg is laid through the time the chick hatches. In a typical galliform bird, the oxygen consumption, in milliliters per hour, can be approximated by
 $c ( t ) = - 0.00272 t ^ { 3 } + 0.138 t ^ { 2 } - 0.8923 t + 0.1499 ( 6 \leq t \leq 30 )$ where t is time (in days) since the egg was laid. (An egg will typically hatch at around $t = 28$ .) Find the total amount of oxygen consumed during the ninth and tenth days ( $t = 8$ to $t = 10$ ). Round your answer to the nearest whole number.

Accepted Answer

A) 64 
B)  18 
C)  50 
D)  1,138 
E)  467 
A) 64 
B)  18 
C)  50 
D)  1,138 
E)  467

Question 4

Decide on what substitution to use, and then evaluate the given integral using a substitution.   $\int 23.1 \sqrt { - 7 x + 9 } \mathrm {~d} x$

Accepted Answer

A)  $2.2 ( - 7 x + 9 ) ^ { \frac { 2 } { 3 } } + C$ 
B)    $- 2.2 \sqrt { - 7 x + 9 } + C$ 
C)    $- 2.2 ( - 7 x + 9 ) ^ { \frac { 3 } { 2 } } + C$ 
D)    $\frac { 80.85 } { \sqrt { - 7 x + 9 } } + C$ 
E)    $- \frac { 80.85 } { \sqrt { - 7 x + 9 } } + C$ 
A)  $2.2 ( - 7 x + 9 ) ^ { \frac { 2 } { 3 } } + C$ 
B)    $- 2.2 \sqrt { - 7 x + 9 } + C$ 
C)    $- 2.2 ( - 7 x + 9 ) ^ { \frac { 3 } { 2 } } + C$ 
D)    $\frac { 80.85 } { \sqrt { - 7 x + 9 } } + C$ 
E)    $- \frac { 80.85 } { \sqrt { - 7 x + 9 } } + C$

Question 5

Evaluate the integral.   $\int \left( \frac { 1 } { v ^ { 9 } } + \frac { 3 } { v } \right) d v$

Accepted Answer

A)  $- \frac { v ^ { - 8 } } { 8 } + 3 \ln ( v ) + C$ 
B)  $\frac { v ^ { - 8 } } { 8 } - 3 \ln | v | + C$ 
C)  $- \frac { v ^ { - 8 } } { 8 } + 3 \ln | v | + C$ 
D)  $- \frac { v ^ { - 10 } } { 10 } - 3 \ln | v | + C$ 
E)  $- \frac { v ^ { - 10 } } { 10 } + 3 \ln ( v ) + C$ 
A)  $- \frac { v ^ { - 8 } } { 8 } + 3 \ln ( v ) + C$ 
B)  $\frac { v ^ { - 8 } } { 8 } - 3 \ln | v | + C$ 
C)  $- \frac { v ^ { - 8 } } { 8 } + 3 \ln | v | + C$ 
D)  $- \frac { v ^ { - 10 } } { 10 } - 3 \ln | v | + C$ 
E)  $- \frac { v ^ { - 10 } } { 10 } + 3 \ln ( v ) + C$

Question 6

Evaluate the integral.  $\int x \left( 5 x ^ { 2 } + 2 \right) ^ { 3 } \mathrm {~d} x$

Accepted Answer

A)   $\frac { ( 5 x + 2 ) ^ { 2 } } { 5 } + C$ 
B)    $\frac { x \left( 5 x ^ { 2 } + 2 \right) ^ { 4 } } { 40 } + C$ 
C)    $\frac { \left( 5 x ^ { 2 } + 2 \right) ^ { 4 } } { 40 } + C$ 
D)   $\frac { \left( 5 x ^ { 2 } + 2 \right) ^ { 4 } } { 20 } + C$ 
E)    $\frac { \left( 5 x ^ { 2 } + 2 \right) ^ { 4 } } { 40 }$ 
A)   $\frac { ( 5 x + 2 ) ^ { 2 } } { 5 } + C$ 
B)    $\frac { x \left( 5 x ^ { 2 } + 2 \right) ^ { 4 } } { 40 } + C$ 
C)    $\frac { \left( 5 x ^ { 2 } + 2 \right) ^ { 4 } } { 40 } + C$ 
D)   $\frac { \left( 5 x ^ { 2 } + 2 \right) ^ { 4 } } { 20 } + C$ 
E)    $\frac { \left( 5 x ^ { 2 } + 2 \right) ^ { 4 } } { 40 }$

Question 7

The graph of the derivative  $f ^ { \prime } ( t )$ of $f ( t )$ is shown. Compute the total change of $f ( t )$ over the interval $[ 2,5 ]$ .

Accepted Answer

A)  $f ( 5 ) - f ( 2 ) = 21$ 
B)    $f ( 5 ) - f ( 2 ) = 7.5$ 
C)   $f ( 5 ) - f ( 2 ) = 5.25$ 
D)    $f ( 5 ) - f ( 2 ) = 2.25$ 
E)    $f ( 5 ) - f ( 2 ) = 10.5$ 
A)  $f ( 5 ) - f ( 2 ) = 21$ 
B)    $f ( 5 ) - f ( 2 ) = 7.5$ 
C)   $f ( 5 ) - f ( 2 ) = 5.25$ 
D)    $f ( 5 ) - f ( 2 ) = 2.25$ 
E)    $f ( 5 ) - f ( 2 ) = 10.5$

Question 8

Evaluate the integral.   $\int _ { 0 } ^ { 2 } 3 x \sqrt { 4 x + 4 } \mathrm {~d} x$

Accepted Answer

A)  $0.5 \left( 2 \cdot 12 ^ { 3 } - 0.1 \cdot \left( 12 ^ { 5 } + 2 ^ { 5 } \right) \right)$ 
B)  $0.5 \left( 2 \cdot 12 + 0.1 \cdot \left( 12 ^ { \frac { 2 } { 3 } } + 2 ^ { \frac { 2 } { 3 } } \right) \right)$ 
C)  $0.5 \left( 2 \cdot 12 ^ { \frac { 3 } { 2 } } - 0.1 \cdot \left( 12 ^ { \frac { 5 } { 2 } } - 4 ^ { \frac { 5 } { 2 } } \right) \right)$ 
D)    $0.5 \left( 2 \cdot 12 ^ { \frac { 1 } { 2 } } - 0.1 \cdot \left( 12 ^ { \frac { 3 } { 2 } } - 4 ^ { \frac { 3 } { 2 } } \right) \right)$ 
E)  $0.5 \left( 2 \cdot 12 ^ { \frac { 3 } { 2 } } - 0.1 \cdot \left( 12 ^ { \frac { 1 } { 2 } } - 4 ^ { \frac { 1 } { 2 } } \right) \right)$ 
A)  $0.5 \left( 2 \cdot 12 ^ { 3 } - 0.1 \cdot \left( 12 ^ { 5 } + 2 ^ { 5 } \right) \right)$ 
B)  $0.5 \left( 2 \cdot 12 + 0.1 \cdot \left( 12 ^ { \frac { 2 } { 3 } } + 2 ^ { \frac { 2 } { 3 } } \right) \right)$ 
C)  $0.5 \left( 2 \cdot 12 ^ { \frac { 3 } { 2 } } - 0.1 \cdot \left( 12 ^ { \frac { 5 } { 2 } } - 4 ^ { \frac { 5 } { 2 } } \right) \right)$ 
D)    $0.5 \left( 2 \cdot 12 ^ { \frac { 1 } { 2 } } - 0.1 \cdot \left( 12 ^ { \frac { 3 } { 2 } } - 4 ^ { \frac { 3 } { 2 } } \right) \right)$ 
E)  $0.5 \left( 2 \cdot 12 ^ { \frac { 3 } { 2 } } - 0.1 \cdot \left( 12 ^ { \frac { 1 } { 2 } } - 4 ^ { \frac { 1 } { 2 } } \right) \right)$

Question 9

Evaluate the integral.   $\int _ { - 1 } ^ { 4 } 3 x e ^ { 2 x ^ { 2 } + 3 } \mathrm {~d} x$

Accepted Answer

A)  $0.75 \left( e ^ { 32 } - e ^ { 2 } \right)$ 
B)  $0.75 \left( e ^ { 35 } - e ^ { 5 } \right)$ 
C)  $0.75 \left( e ^ { 35 } + e ^ { 5 } \right)$ 
D)  $1.75 \left( e ^ { 35 } + e ^ { 5 } \right)$ 
E)  $1.75 \left( e ^ { 35 } - e ^ { 5 } \right)$ 
A)  $0.75 \left( e ^ { 32 } - e ^ { 2 } \right)$ 
B)  $0.75 \left( e ^ { 35 } - e ^ { 5 } \right)$ 
C)  $0.75 \left( e ^ { 35 } + e ^ { 5 } \right)$ 
D)  $1.75 \left( e ^ { 35 } + e ^ { 5 } \right)$ 
E)  $1.75 \left( e ^ { 35 } - e ^ { 5 } \right)$

Question 10

Evaluate the integral.   $\int x ^ { - 9 } d x$

Accepted Answer

A)  $- \frac { x ^ { - 10 } } { 8 } + C$ 
B)  $- \frac { x ^ { - 10 } } { 10 } + C$ 
C)  $- \frac { x ^ { - 8 } } { 8 } + C$ 
D)  $\frac { x ^ { - 10 } } { 10 } + C$ 
E)  $\frac { x ^ { - 8 } } { 8 } + C$ 
A)  $- \frac { x ^ { - 10 } } { 8 } + C$ 
B)  $- \frac { x ^ { - 10 } } { 10 } + C$ 
C)  $- \frac { x ^ { - 8 } } { 8 } + C$ 
D)  $\frac { x ^ { - 10 } } { 10 } + C$ 
E)  $\frac { x ^ { - 8 } } { 8 } + C$

Question 11

Evaluate the integral.   $\int _ { 0 } ^ { \sqrt { 2 } } 2 x \sqrt { x ^ { 2 } + 9 } \mathrm {~d} x$

Accepted Answer

A)  $\frac { 2 } { 3 } \left( 11 ^ { \frac { 3 } { 2 } } - 27 \right)$ 
B)  $- \frac { 2 \cdot 11 ^ { \frac { 2 } { 3 } } } { 3 }$ 
C)  $\frac { 2 \cdot 11 ^ { \frac { 3 } { 2 } } } { 3 }$ 
D)  $\frac { 2 } { 3 } \left( 27 - 11 ^ { \frac { 3 } { 2 } } \right)$ 
E)  $\frac { 2 } { 3 } \left( 11 ^ { \frac { 2 } { 3 } } - 27 \right)$ 
A)  $\frac { 2 } { 3 } \left( 11 ^ { \frac { 3 } { 2 } } - 27 \right)$ 
B)  $- \frac { 2 \cdot 11 ^ { \frac { 2 } { 3 } } } { 3 }$ 
C)  $\frac { 2 \cdot 11 ^ { \frac { 3 } { 2 } } } { 3 }$ 
D)  $\frac { 2 } { 3 } \left( 27 - 11 ^ { \frac { 3 } { 2 } } \right)$ 
E)  $\frac { 2 } { 3 } \left( 11 ^ { \frac { 2 } { 3 } } - 27 \right)$

Question 12

Evaluate the integral.  $\int _ { - 3 } ^ { 3 } \left( x ^ { 2 } + 98 \right) \mathrm { d } x$

Accepted Answer

A) 642 
B)  615 
C)  18 
D)  606 
E)  588 
A) 642 
B)  615 
C)  18 
D)  606 
E)  588

Question 13

Evaluate the integral.   $\int _ { - 1 } ^ { 1 } 3 ^ { x - 3 } \mathrm {~d} x$

Accepted Answer

A)  $\frac { 8 } { 81 \log _ { 2 } 3 }$ 
B)  $\frac { 81 } { 8 \ln 3 }$ 
C)  $\frac { 81 } { 8 }$ 
D)  $\frac { 81 } { 8 \log _ { 2 } 3 }$ 
E)  $\frac { 8 } { 81 \ln 3 }$ 
A)  $\frac { 8 } { 81 \log _ { 2 } 3 }$ 
B)  $\frac { 81 } { 8 \ln 3 }$ 
C)  $\frac { 81 } { 8 }$ 
D)  $\frac { 81 } { 8 \log _ { 2 } 3 }$ 
E)  $\frac { 8 } { 81 \ln 3 }$

Question 14

Evaluate the integral.  
  $\int ( 3 x + 5 ) ^ { 5 } \mathrm {~d} x$

Accepted Answer

A)   $\frac { ( 3 x + 5 ) ^ { 6 } } { 18 }$ 
B)    $\frac { ( 3 x + 5 ) ^ { 6 } } { 18 } + C$ 
C)    $\frac { ( 3 x + 5 x ) ^ { 6 } } { 6 } + C$ 
D)    $\frac { ( 3 x + 5 ) ^ { 6 } } { 3 } + C$ 
E)    $\frac { ( 3 x + 5 ) ^ { 6 } } { 6 } + C$ 
A)   $\frac { ( 3 x + 5 ) ^ { 6 } } { 18 }$ 
B)    $\frac { ( 3 x + 5 ) ^ { 6 } } { 18 } + C$ 
C)    $\frac { ( 3 x + 5 x ) ^ { 6 } } { 6 } + C$ 
D)    $\frac { ( 3 x + 5 ) ^ { 6 } } { 3 } + C$ 
E)    $\frac { ( 3 x + 5 ) ^ { 6 } } { 6 } + C$

Question 15

Calculate the Riemann Sum for the integral using n = 5. Round your answers to the two decimal places.   $\int _ { - 5 } ^ { 10 } e ^ { - x } d x$

Accepted Answer

A) 156.19 
B)  468.57 
C)  148.41 
D)  7.78 
E)  23.33 
A) 156.19 
B)  468.57 
C)  148.41 
D)  7.78 
E)  23.33

Question 16

Evaluate the integral.  $\int x ^ { 7 } d x$

Accepted Answer

A)  $7 x ^ { 8 } + C$ 
B)  $\frac { x ^ { 8 } } { 8 }$ 
C)  $7 x ^ { 49 }$ 
D)  1 
E)  $\frac { x ^ { 8 } } { 8 } + C$ 
A)  $7 x ^ { 8 } + C$ 
B)  $\frac { x ^ { 8 } } { 8 }$ 
C)  $7 x ^ { 49 }$ 
D)  1 
E)  $\frac { x ^ { 8 } } { 8 } + C$

Question 17

Find $f ( x )$ if $f ( 1 ) = \frac { 11 } { 2 }$ and the tangent line at $( x , f ( x ) )$ has the slope $11 x e ^ { x ^ { 2 } - 1 }$ .

Accepted Answer

A)   $\frac { 11 } { 2 } e ^ { x ^ { 2 } - 1 } + \frac { 11 } { 2 }$ 
B)   $\frac { 1 } { 2 } e ^ { x ^ { 2 } - 1 } + C$ 
C)   $\frac { 1 } { 2 } e ^ { x ^ { 2 } - 1 }$ 
D)   $\frac { 11 } { 2 } e ^ { x ^ { 2 } - 1 }$ 
E)    $11 e ^ { x ^ { 2 } - 1 }$ 
A)   $\frac { 11 } { 2 } e ^ { x ^ { 2 } - 1 } + \frac { 11 } { 2 }$ 
B)   $\frac { 1 } { 2 } e ^ { x ^ { 2 } - 1 } + C$ 
C)   $\frac { 1 } { 2 } e ^ { x ^ { 2 } - 1 }$ 
D)   $\frac { 11 } { 2 } e ^ { x ^ { 2 } - 1 }$ 
E)    $11 e ^ { x ^ { 2 } - 1 }$

Question 18

Evaluate the integral.  $\int ( - 8 x + 4 ) ^ { - 2 } d x$

Accepted Answer

A)   $\frac { \left( - 8 x ^ { 2 } + 4 \right) ^ { - 1 } } { 8 } + C$ 
B)    $\frac { ( - 8 x + 4 ) ^ { - 1 } } { 8 } + C$ 
C)    $\frac { ( - 8 x + 4 ) ^ { - 3 } } { 16 } + C$ 
D)    $\frac { ( - 8 x + 4 ) ^ { - 3 } } { 8 } + C$ 
E)    $\frac { ( - 8 x + 4 ) ^ { - 1 } } { 16 } + C$ 
A)   $\frac { \left( - 8 x ^ { 2 } + 4 \right) ^ { - 1 } } { 8 } + C$ 
B)    $\frac { ( - 8 x + 4 ) ^ { - 1 } } { 8 } + C$ 
C)    $\frac { ( - 8 x + 4 ) ^ { - 3 } } { 16 } + C$ 
D)    $\frac { ( - 8 x + 4 ) ^ { - 3 } } { 8 } + C$ 
E)    $\frac { ( - 8 x + 4 ) ^ { - 1 } } { 16 } + C$

Question 19

Evaluate the integral.   $\int _ { - 1.2 } ^ { 2 } 4 e ^ { x - 3 } \mathrm {~d} x$

Accepted Answer

A)  $\left( e ^ { - 1 } - e ^ { - 4.2 } \right)$ 
B)  $4 \left( e ^ { - 1 } - e ^ { - 1.2 } \right)$ 
C)  $4 \left( e ^ { - 1 } + e ^ { - 4.2 } \right)$ 
D)  $4 \left( e ^ { 2 } - e ^ { - 4.2 } \right)$ 
E)  $4 \left( e ^ { - 1 } - e ^ { - 4.2 } \right)$ 
A)  $\left( e ^ { - 1 } - e ^ { - 4.2 } \right)$ 
B)  $4 \left( e ^ { - 1 } - e ^ { - 1.2 } \right)$ 
C)  $4 \left( e ^ { - 1 } + e ^ { - 4.2 } \right)$ 
D)  $4 \left( e ^ { 2 } - e ^ { - 4.2 } \right)$ 
E)  $4 \left( e ^ { - 1 } - e ^ { - 4.2 } \right)$

Question 20

Evaluate the integral.
​
​ $\int ( 6 x + 9 ) ^ { 5 } \mathrm {~d} x$

Accepted Answer

The answer of Evaluate the integral.
​
​ \(\int ( 6 x...

Evaluate the integral. $\int \left( \frac { 4 } { x ^ { 0.2 } } - \frac { 5 } { x ^ { 1.1 } } \right) d x$

A race car has a velocity of $v ( t ) = 600 \left( 1 - e ^ { - 1.6 t } \right) \frac { \mathrm { ft } } { \mathrm { s } }$ , t seconds after starting. Use a Riemann sum with n = 10 to estimate how far the car travels in the first 2 seconds. (Round your answer to the nearest whole number.)

Decide on what substitution to use, and then evaluate the given integral using a substitution. $\int 23.1 \sqrt { - 7 x + 9 } \mathrm {~d} x$

Evaluate the integral. $\int \left( \frac { 1 } { v ^ { 9 } } + \frac { 3 } { v } \right) d v$

Evaluate the integral. $\int x \left( 5 x ^ { 2 } + 2 \right) ^ { 3 } \mathrm {~d} x$

The graph of the derivative $f ^ { \prime } ( t )$ of $f ( t )$ is shown. Compute the total change of $f ( t )$ over the interval $[ 2,5 ]$ . $The graph of the derivative f ^ { \prime } ( t ) of f ( t ) is shown. Compute the total change of f ( t ) over the interval [ 2,5 ] .$

Evaluate the integral. $\int _ { 0 } ^ { 2 } 3 x \sqrt { 4 x + 4 } \mathrm {~d} x$

Evaluate the integral. $\int _ { - 1 } ^ { 4 } 3 x e ^ { 2 x ^ { 2 } + 3 } \mathrm {~d} x$

Evaluate the integral. $\int x ^ { - 9 } d x$

Evaluate the integral. $\int _ { 0 } ^ { \sqrt { 2 } } 2 x \sqrt { x ^ { 2 } + 9 } \mathrm {~d} x$

Evaluate the integral. $\int _ { - 3 } ^ { 3 } \left( x ^ { 2 } + 98 \right) \mathrm { d } x$

Evaluate the integral. $\int _ { - 1 } ^ { 1 } 3 ^ { x - 3 } \mathrm {~d} x$

Evaluate the integral. $\int ( 3 x + 5 ) ^ { 5 } \mathrm {~d} x$

Calculate the Riemann Sum for the integral using n = 5. Round your answers to the two decimal places. $\int _ { - 5 } ^ { 10 } e ^ { - x } d x$

Evaluate the integral. $\int x ^ { 7 } d x$

Find $f ( x )$ if $f ( 1 ) = \frac { 11 } { 2 }$ and the tangent line at $( x , f ( x ) )$ has the slope $11 x e ^ { x ^ { 2 } - 1 }$ .

Evaluate the integral. $\int ( - 8 x + 4 ) ^ { - 2 } d x$

Evaluate the integral. $\int _ { - 1.2 } ^ { 2 } 4 e ^ { x - 3 } \mathrm {~d} x$

Evaluate the integral. $\int ( 6 x + 9 ) ^ { 5 } \mathrm {~d} x$

Functions and Applications

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Introduction to the Derivative

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Exam 13: The Integral

Evaluate the integral. ∫(4x0.2−5x1.1)dx\int \left( \frac { 4 } { x ^ { 0.2 } } - \frac { 5 } { x ^ { 1.1 } } \right) d x∫(x0.24​−x1.15​)dx

Decide on what substitution to use, and then evaluate the given integral using a substitution. ∫23.1−7x+9 dx\int 23.1 \sqrt { - 7 x + 9 } \mathrm {~d} x∫23.1−7x+9​ dx

Evaluate the integral. ∫(1v9+3v)dv\int \left( \frac { 1 } { v ^ { 9 } } + \frac { 3 } { v } \right) d v∫(v91​+v3​)dv

Evaluate the integral. ∫x(5x2+2)3 dx\int x \left( 5 x ^ { 2 } + 2 \right) ^ { 3 } \mathrm {~d} x∫x(5x2+2)3 dx

The graph of the derivative f′(t)f ^ { \prime } ( t )f′(t) of f(t)f ( t )f(t) is shown. Compute the total change of f(t)f ( t )f(t) over the interval [2,5][ 2,5 ][2,5] .

Evaluate the integral. ∫023x4x+4 dx\int _ { 0 } ^ { 2 } 3 x \sqrt { 4 x + 4 } \mathrm {~d} x∫02​3x4x+4​ dx

Evaluate the integral. ∫−143xe2x2+3 dx\int _ { - 1 } ^ { 4 } 3 x e ^ { 2 x ^ { 2 } + 3 } \mathrm {~d} x∫−14​3xe2x2+3 dx

Evaluate the integral. ∫x−9dx\int x ^ { - 9 } d x∫x−9dx

Evaluate the integral. ∫022xx2+9 dx\int _ { 0 } ^ { \sqrt { 2 } } 2 x \sqrt { x ^ { 2 } + 9 } \mathrm {~d} x∫02​​2xx2+9​ dx

Evaluate the integral. ∫−33(x2+98)dx\int _ { - 3 } ^ { 3 } \left( x ^ { 2 } + 98 \right) \mathrm { d } x∫−33​(x2+98)dx

Evaluate the integral. ∫−113x−3 dx\int _ { - 1 } ^ { 1 } 3 ^ { x - 3 } \mathrm {~d} x∫−11​3x−3 dx

Evaluate the integral. ∫(3x+5)5 dx\int ( 3 x + 5 ) ^ { 5 } \mathrm {~d} x∫(3x+5)5 dx

Calculate the Riemann Sum for the integral using n = 5. Round your answers to the two decimal places. ∫−510e−xdx\int _ { - 5 } ^ { 10 } e ^ { - x } d x∫−510​e−xdx

Evaluate the integral. ∫x7dx\int x ^ { 7 } d x∫x7dx

Find f(x)f ( x )f(x) if f(1)=112f ( 1 ) = \frac { 11 } { 2 }f(1)=211​ and the tangent line at (x,f(x))( x , f ( x ) )(x,f(x)) has the slope 11xex2−111 x e ^ { x ^ { 2 } - 1 }11xex2−1 .

Evaluate the integral. ∫(−8x+4)−2dx\int ( - 8 x + 4 ) ^ { - 2 } d x∫(−8x+4)−2dx

Evaluate the integral. ∫−1.224ex−3 dx\int _ { - 1.2 } ^ { 2 } 4 e ^ { x - 3 } \mathrm {~d} x∫−1.22​4ex−3 dx

Evaluate the integral. ​ ​ ∫(6x+9)5 dx\int ( 6 x + 9 ) ^ { 5 } \mathrm {~d} x∫(6x+9)5 dx

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

Evaluate the integral. $\int \left( \frac { 4 } { x ^ { 0.2 } } - \frac { 5 } { x ^ { 1.1 } } \right) d x$

Decide on what substitution to use, and then evaluate the given integral using a substitution. $\int 23.1 \sqrt { - 7 x + 9 } \mathrm {~d} x$

Evaluate the integral. $\int \left( \frac { 1 } { v ^ { 9 } } + \frac { 3 } { v } \right) d v$

Evaluate the integral. $\int x \left( 5 x ^ { 2 } + 2 \right) ^ { 3 } \mathrm {~d} x$

The graph of the derivative $f ^ { \prime } ( t )$ of $f ( t )$ is shown. Compute the total change of $f ( t )$ over the interval $[ 2,5 ]$ . $The graph of the derivative f ^ { \prime } ( t ) of f ( t ) is shown. Compute the total change of f ( t ) over the interval [ 2,5 ] .$

Evaluate the integral. $\int _ { 0 } ^ { 2 } 3 x \sqrt { 4 x + 4 } \mathrm {~d} x$

Evaluate the integral. $\int _ { - 1 } ^ { 4 } 3 x e ^ { 2 x ^ { 2 } + 3 } \mathrm {~d} x$

Evaluate the integral. $\int x ^ { - 9 } d x$

Evaluate the integral. $\int _ { 0 } ^ { \sqrt { 2 } } 2 x \sqrt { x ^ { 2 } + 9 } \mathrm {~d} x$

Evaluate the integral. $\int _ { - 3 } ^ { 3 } \left( x ^ { 2 } + 98 \right) \mathrm { d } x$

Evaluate the integral. $\int _ { - 1 } ^ { 1 } 3 ^ { x - 3 } \mathrm {~d} x$

Evaluate the integral. $\int ( 3 x + 5 ) ^ { 5 } \mathrm {~d} x$

Calculate the Riemann Sum for the integral using n = 5. Round your answers to the two decimal places. $\int _ { - 5 } ^ { 10 } e ^ { - x } d x$

Evaluate the integral. $\int x ^ { 7 } d x$

Find $f ( x )$ if $f ( 1 ) = \frac { 11 } { 2 }$ and the tangent line at $( x , f ( x ) )$ has the slope $11 x e ^ { x ^ { 2 } - 1 }$ .

Evaluate the integral. $\int ( - 8 x + 4 ) ^ { - 2 } d x$

Evaluate the integral. $\int _ { - 1.2 } ^ { 2 } 4 e ^ { x - 3 } \mathrm {~d} x$

Evaluate the integral. $\int ( 6 x + 9 ) ^ { 5 } \mathrm {~d} x$