Question 1

The velocity of a particle moving in a straight line is given by $v = t \left( t ^ { 2 } + 6 \right) ^ { 4 } + 3 t$ .  
Find an expression for the position s after time t.

Accepted Answer

A)  $s ( t ) = \frac { \left( t ^ { 2 } + 6 \right) ^ { 5 } } { 10 } + 3 t ^ { 2 } + C$ 
B)    $s ( t ) = \frac { \left( t ^ { 2 } + 6 \right) ^ { 5 } } { 5 } + \frac { 3 t ^ { 2 } } { 2 } + C$ 
C)    $s ( t ) = \frac { \left( t ^ { 2 } + 6 \right) ^ { 5 } } { 10 } + \frac { 3 t ^ { 2 } } { 2 } + C$ 
D)    $s ( t ) = \frac { t \left( t ^ { 2 } + 6 \right) ^ { 5 } } { 10 } + \frac { 3 t ^ { 2 } } { 2 } + C$ 
E)    $s ( t ) = \frac { \left( t ^ { 2 } + 6 \right) ^ { 5 } } { 10 } + \frac { 3 t } { 2 } + C$ 
A)  $s ( t ) = \frac { \left( t ^ { 2 } + 6 \right) ^ { 5 } } { 10 } + 3 t ^ { 2 } + C$ 
B)    $s ( t ) = \frac { \left( t ^ { 2 } + 6 \right) ^ { 5 } } { 5 } + \frac { 3 t ^ { 2 } } { 2 } + C$ 
C)    $s ( t ) = \frac { \left( t ^ { 2 } + 6 \right) ^ { 5 } } { 10 } + \frac { 3 t ^ { 2 } } { 2 } + C$ 
D)    $s ( t ) = \frac { t \left( t ^ { 2 } + 6 \right) ^ { 5 } } { 10 } + \frac { 3 t ^ { 2 } } { 2 } + C$ 
E)    $s ( t ) = \frac { \left( t ^ { 2 } + 6 \right) ^ { 5 } } { 10 } + \frac { 3 t } { 2 } + C$

Question 2

Evaluate the integral.  
  $\int \frac { e ^ { - 0.05 x } } { 1 - e ^ { - 0.05 x } } \mathrm {~d} x$

Accepted Answer

A)   $\frac { \ln \left| 1 - e ^ { - 0.05 x } \right| } { 20 } - x + C$ 
B)    $- 20 \ln \left| 1 - e ^ { - 0.05 x } \right| + x + C$ 
C)    $20 \ln \left| 1 - e ^ { - 0.05 x } \right| - x + C$ 
D)    $0.05 \ln \left| 1 - e ^ { - 0.05 x } \right| + x + C$ 
E)    $- 0.05 \ln \left| 1 - e ^ { - 0.05 x } \right| - x + C$ 
A)   $\frac { \ln \left| 1 - e ^ { - 0.05 x } \right| } { 20 } - x + C$ 
B)    $- 20 \ln \left| 1 - e ^ { - 0.05 x } \right| + x + C$ 
C)    $20 \ln \left| 1 - e ^ { - 0.05 x } \right| - x + C$ 
D)    $0.05 \ln \left| 1 - e ^ { - 0.05 x } \right| + x + C$ 
E)    $- 0.05 \ln \left| 1 - e ^ { - 0.05 x } \right| - x + C$

Question 3

Evaluate the integral.  $\int _ { 6 } ^ { 10 } 42 e ^ { x } d x$

Accepted Answer

A)  $42 \left( e ^ { 11 } - e ^ { 7 } \right)$ 
B)  $42 \left( e ^ { 9 } + e ^ { 5 } \right)$ 
C)  $\left( e ^ { 10 } - e ^ { 6 } \right)$ 
D)  $42 e ^ { 4 }$ 
E)  $42 \left( e ^ { 10 } - e ^ { 6 } \right)$ 
A)  $42 \left( e ^ { 11 } - e ^ { 7 } \right)$ 
B)  $42 \left( e ^ { 9 } + e ^ { 5 } \right)$ 
C)  $\left( e ^ { 10 } - e ^ { 6 } \right)$ 
D)  $42 e ^ { 4 }$ 
E)  $42 \left( e ^ { 10 } - e ^ { 6 } \right)$

Question 4

Evaluate the integral.  $\int _ { 4 } ^ { 9 } 3 \sqrt { x } \mathrm {~d} x$

Accepted Answer

A) 38 
B)  85.5 
C)  10 
D)  19 
E)  2 
A) 38 
B)  85.5 
C)  10 
D)  19 
E)  2

Question 5

Calculate the Riemann Sum for the integral using n = 4.
​ $\int _ { - 4 } ^ { 0 } x ^ { 2 } d x$

Accepted Answer

The answer of Calculate the Riemann Sum for the integral...

Question 6

The normal distribution curve which models, distributions of data in a wide range of applications, is given by the function 
$p ( x ) = \frac { 1 } { \sqrt { 2 \pi } } e ^ { - ( x - \mu ) ^ { 2 } / 2 \delta ^ { 2 } }$ where $\pi = 3.14159265 \ldots$ and $     \sigma   $ and $     \mu   $ are constants called the standard deviation and the mean, respectively. Its graph is shown in the figure.    ?
In a survey, consumers were asked to rate a new toothpaste on a scale of 1-10. The resulting data are modeled by a normal distribution with $\mu = 4.1$ and $\sigma = 1.2$ . The percentage of consumers who gave the toothpaste a score between a and b on the section is given by $\int _ { a } ^ { b } p ( x ) d x$  
Use a Riemann sum with n = 10 to estimate the percentage of customers who rated the toothpaste 5 or higher. (Use the range 4.5 to 10.5.) Round your answer to the nearest whole number.

Accepted Answer

A) 45% 
B)  46% 
C)  47% 
D)  48% 
E)  49% 
A) 45% 
B)  46% 
C)  47% 
D)  48% 
E)  49%

The velocity of a particle moving in a straight line is given by $v = t \left( t ^ { 2 } + 6 \right) ^ { 4 } + 3 t$ . Find an expression for the position s after time t.

Evaluate the integral. $\int \frac { e ^ { - 0.05 x } } { 1 - e ^ { - 0.05 x } } \mathrm {~d} x$

Evaluate the integral. $\int _ { 6 } ^ { 10 } 42 e ^ { x } d x$

Evaluate the integral. $\int _ { 4 } ^ { 9 } 3 \sqrt { x } \mathrm {~d} x$

Calculate the Riemann Sum for the integral using n = 4. $\int _ { - 4 } ^ { 0 } x ^ { 2 } d x$

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

Exam 13: The Integral

The velocity of a particle moving in a straight line is given by v=t(t2+6)4+3tv = t \left( t ^ { 2 } + 6 \right) ^ { 4 } + 3 tv=t(t2+6)4+3t . Find an expression for the position s after time t.

Evaluate the integral. ∫e−0.05x1−e−0.05x dx\int \frac { e ^ { - 0.05 x } } { 1 - e ^ { - 0.05 x } } \mathrm {~d} x∫1−e−0.05xe−0.05x​ dx

Evaluate the integral. ∫61042exdx\int _ { 6 } ^ { 10 } 42 e ^ { x } d x∫610​42exdx

Evaluate the integral. ∫493x dx\int _ { 4 } ^ { 9 } 3 \sqrt { x } \mathrm {~d} x∫49​3x​ dx

Calculate the Riemann Sum for the integral using n = 4. ​ ∫−40x2dx\int _ { - 4 } ^ { 0 } x ^ { 2 } d x∫−40​x2dx