Question 1

Find the area of the shaded region.
-

Accepted Answer

A)  4.7 
B)  7.4 
C)  5.4 
D)  2.7 
A)  4.7 
B)  7.4 
C)  5.4 
D)  2.7

Question 2

Find the integral.
-$\int\left(\frac{1}{x}+\frac{2}{x^{2}}+\frac{3}{x^{3}}\right) d x$

Accepted Answer

A)  $2 x+2 \ln \left|x^{2}\right|+3 \ln \left|x^{3}\right|+C$ 
B)  $\ln |x|+2 \ln \left|x^{2}\right|+3 \ln \left|x^{3}\right|+C$ 
C)  $\ln |x|-2 x^{-1}-\frac{3}{2 x^{-2}}+C$ 
D)  $\frac{2}{x^{2}}+\frac{6}{x^{3}}+\frac{12}{x^{4}}+C$ 
A)  $2 x+2 \ln \left|x^{2}\right|+3 \ln \left|x^{3}\right|+C$ 
B)  $\ln |x|+2 \ln \left|x^{2}\right|+3 \ln \left|x^{3}\right|+C$ 
C)  $\ln |x|-2 x^{-1}-\frac{3}{2 x^{-2}}+C$ 
D)  $\frac{2}{x^{2}}+\frac{6}{x^{3}}+\frac{12}{x^{4}}+C$

Question 3

Evaluate.
-$\int\left(4 t^{2}+4 t-5\right) d t$

Accepted Answer

A)  $\frac{4}{3} t^{3}+2 t^{2}-5 t+C$ 
B)  $8 t+4+C$ 
C)  $4 t^{3}+4 t^{2}-5 t+C$ 
D)  $2 t^{3}+4 t^{2}-5 t+C$ 
A)  $\frac{4}{3} t^{3}+2 t^{2}-5 t+C$ 
B)  $8 t+4+C$ 
C)  $4 t^{3}+4 t^{2}-5 t+C$ 
D)  $2 t^{3}+4 t^{2}-5 t+C$

Question 4

Solve the problem.
-Suppose that a velocity function is given by $v(t)=2 t^{4}$. Find the position function $s(t)$ if $s(0)=7$.

Accepted Answer

A)  $s(t)=\frac{2}{5} t^{5}+7$ 
B)  $s(t)=2 t^{5}+7$ 
C)  $s(t)=\frac{2}{5} t^{5}$ 
D)  $s(t)=8 t^{3}+7$ 
A)  $s(t)=\frac{2}{5} t^{5}+7$ 
B)  $s(t)=2 t^{5}+7$ 
C)  $s(t)=\frac{2}{5} t^{5}$ 
D)  $s(t)=8 t^{3}+7$

Question 5

Solve the problem.
-Assume that the rate of change of the population of a certain city is given by $\frac{d y}{d t}=6000 e^{.06 t}$, where $y$ is the population at time $t$, in years. The population was 100,000 in 1980 . Assume $t=0$ is 1980. Predict the population in 1985 .

Accepted Answer

A)  $4.4 \times 10^{5}$ 
B)  $1.4 \times 10^{5}$ 
C)  $1.3 \times 10^{5}$ 
D)  $1.0 \times 10^{5}$ 
A)  $4.4 \times 10^{5}$ 
B)  $1.4 \times 10^{5}$ 
C)  $1.3 \times 10^{5}$ 
D)  $1.0 \times 10^{5}$

Question 6

Find the integral.
-$\int(y-1)^{7} d y$

Accepted Answer

A)  $\frac{1}{2} y^{2}+\frac{1}{8}(y-1)^{8}+C$ 
B)  $\frac{1}{16(y-1)^{8}}+C$ 
C)  $\frac{1}{9}(y-1)^{9}+\frac{1}{8}(y-1)^{8}+C$ 
D)  $\frac{1}{8}(y-1)^{8}+C$ 
A)  $\frac{1}{2} y^{2}+\frac{1}{8}(y-1)^{8}+C$ 
B)  $\frac{1}{16(y-1)^{8}}+C$ 
C)  $\frac{1}{9}(y-1)^{9}+\frac{1}{8}(y-1)^{8}+C$ 
D)  $\frac{1}{8}(y-1)^{8}+C$

Question 7

Find the integral.
-$\int 8 e^{4 y} d y$

Accepted Answer

A)  $4 e^{4 y}+C$ 
B)  $\frac{1}{4} e^{4 y}+C$ 
C)  $2 e^{4 y}+C$ 
D)  $\frac{1}{2} e^{4 y}+C$ 
A)  $4 e^{4 y}+C$ 
B)  $\frac{1}{4} e^{4 y}+C$ 
C)  $2 e^{4 y}+C$ 
D)  $\frac{1}{2} e^{4 y}+C$

Question 8

Approximate the area under the curve and above the $x$-axis using $n$ rectangles. Let the height of each rectangle be given by the value of the function at the right side of the rectangle.
-$f(x)=x^{2}-3 x+4$ from $x=1$ to $x=5 ; n=4$

Accepted Answer

A)  38 
B)  28 
C)  48 
D)  18 
A)  38 
B)  28 
C)  48 
D)  18

Question 9

Find the area bounded by the given curves.
-$x=0, x=1, y=x^{2}+6, y=x^{2}+2$

Accepted Answer

A)  16 
B)  4 
C)  8 
D)  12 
A)  16 
B)  4 
C)  8 
D)  12

Question 10

Find the integral.
-$\int\left(3 x+5 x^{-1}\right) d x$

Accepted Answer

A)  $3 x^{3}+30 x-\frac{25}{3} x^{-1}+C$ 
B)  $3 x^{3}+15 x-\frac{25}{3} x^{-1}+C$ 
C)  $\frac{3}{2} x^{2}+5 \ln |x|+C$ 
D)  $\frac{9}{4} x^{4}+25 \ln \left|x^{2}\right|+C$ 
A)  $3 x^{3}+30 x-\frac{25}{3} x^{-1}+C$ 
B)  $3 x^{3}+15 x-\frac{25}{3} x^{-1}+C$ 
C)  $\frac{3}{2} x^{2}+5 \ln |x|+C$ 
D)  $\frac{9}{4} x^{4}+25 \ln \left|x^{2}\right|+C$

Question 11

Evaluate.
-$\int 10^{2 x} d x$

Accepted Answer

A)  $\frac{10^{2 x}}{\ln 10}+C$ 
B)  $\frac{10^{2 x}}{2}+C$ 
C)  $\frac{10^{3 x}}{3}+C$ 
D)  $\frac{10^{2 x}}{2 \ln 10}+C$ 
A)  $\frac{10^{2 x}}{\ln 10}+C$ 
B)  $\frac{10^{2 x}}{2}+C$ 
C)  $\frac{10^{3 x}}{3}+C$ 
D)  $\frac{10^{2 x}}{2 \ln 10}+C$

Question 12

Evaluate the definite integral.
-$\int_{0}^{1} \frac{1}{13 x+4} d x$

Accepted Answer

A)  $\frac{1}{13}(\ln 13-\ln 4)$ 
B)  $\frac{1}{13} \ln |13 x+4|$ 
C)  $\frac{1}{13} \ln \frac{17}{4}$ 
D)  $\frac{1}{13} \ln 13$ 
A)  $\frac{1}{13}(\ln 13-\ln 4)$ 
B)  $\frac{1}{13} \ln |13 x+4|$ 
C)  $\frac{1}{13} \ln \frac{17}{4}$ 
D)  $\frac{1}{13} \ln 13$

Question 13

Find the general solution of the differential equation.
-$\frac{d y}{d x}=63 x^{2}-6 x$

Accepted Answer

A)  $63 x^{3}-6 x^{2}+C$ 
B)  $21 x^{3}-6 x^{2}+C$ 
C)  $63 x^{3}-3 x^{2}+C$ 
D)  $21 x^{3}-3 x^{2}+C$ 
A)  $63 x^{3}-6 x^{2}+C$ 
B)  $21 x^{3}-6 x^{2}+C$ 
C)  $63 x^{3}-3 x^{2}+C$ 
D)  $21 x^{3}-3 x^{2}+C$

Question 14

Estimate the value of the quantity
-The graph below shows the rate of natural gas usage (in therms per day) in one household for a 30 -day period. Estimate the total number of therms used during this period. Use left endpoints and rectangles with widths of 3 days.

Accepted Answer

A)  165 therms 
B)  147 therms 
C)  159 therms 
D)  136 therms 
A)  165 therms 
B)  147 therms 
C)  159 therms 
D)  136 therms

Question 15

Estimate the value of the quantity
-The table gives dye concentrations for a cardiac-output determination. The amount of dye injected was $5.7 \mathrm{mg}$. Plot the data and connect the data points with a smooth curve. Find the area under the curve using rectangles. Use this area to estimate the cardiac output.

Accepted Answer

A)  $0.2 \mathrm{~L} / \mathrm{min}$ 
B)  $334.7 \mathrm{~L} / \mathrm{min}$ 
C)  $21.5 \mathrm{~L} / \mathrm{min}$ 
D)  $10.8 \mathrm{~L} / \mathrm{min}$ 
A)  $0.2 \mathrm{~L} / \mathrm{min}$ 
B)  $334.7 \mathrm{~L} / \mathrm{min}$ 
C)  $21.5 \mathrm{~L} / \mathrm{min}$ 
D)  $10.8 \mathrm{~L} / \mathrm{min}$

Question 16

Write the word or phrase that best completes each statement or answers thequestion.
-A student sees $\int \frac{e^{x}}{e^{2 x}-16} d x$ worked on the board using $-\int \frac{d u}{a^{2}-u^{2}}$, where $u=e^{x}$
and $d u=e^{x} d x$. The student sees $\int \frac{e^{x}}{e^{x}-9} d x$ on a test. Can the same formula be used?

Accepted Answer

No, the st

Question 17

Find the integral.
-$\int \frac{x d x}{\left(7 x^{2}+3\right)^{5}}$

Accepted Answer

A)  $-\frac{7}{3}\left(7 x^{2}+3\right)^{-4}+C$ 
B)  $-\frac{1}{14}\left(7 x^{2}+3\right)^{-6}+C$ 
C)  $-\frac{7}{3}\left(7 x^{2}+3\right)^{-6}+C$ 
D)  $-\frac{1}{56}\left(7 x^{2}+3\right)^{-4}+C$ 
A)  $-\frac{7}{3}\left(7 x^{2}+3\right)^{-4}+C$ 
B)  $-\frac{1}{14}\left(7 x^{2}+3\right)^{-6}+C$ 
C)  $-\frac{7}{3}\left(7 x^{2}+3\right)^{-6}+C$ 
D)  $-\frac{1}{56}\left(7 x^{2}+3\right)^{-4}+C$

Question 18

Find the integral.
-$\int\left(7 x^{-4}-9 x^{-1}\right) d x$

Accepted Answer

A)  $-\frac{7}{3} x^{-3}-9 \ln |x|+C$ 
B)  $-\frac{7}{3} x^{-3}+9 \ln |x|+C$ 
C)  $\frac{7}{4} x^{-3}+9 \ln |x|+C$ 
D)  $\frac{7}{4} x^{-3}-9 \ln |x|+C$ 
A)  $-\frac{7}{3} x^{-3}-9 \ln |x|+C$ 
B)  $-\frac{7}{3} x^{-3}+9 \ln |x|+C$ 
C)  $\frac{7}{4} x^{-3}+9 \ln |x|+C$ 
D)  $\frac{7}{4} x^{-3}-9 \ln |x|+C$

Question 19

Use integration by parts to find the integral.
-$\int 7 x \ln x d x$

Accepted Answer

A)  $\frac{x^{2}}{2} \ln x-\frac{x^{2}}{4}+C$ 
B)  $\frac{7}{2} x^{2} \ln x-\frac{7}{4} x^{2}+C$ 
C)  $\frac{7}{2} x \ln x-\frac{7}{4} x+C$ 
D)  $\frac{7}{2} x^{2} \ln x-\frac{x^{2}}{4}+C$ 
A)  $\frac{x^{2}}{2} \ln x-\frac{x^{2}}{4}+C$ 
B)  $\frac{7}{2} x^{2} \ln x-\frac{7}{4} x^{2}+C$ 
C)  $\frac{7}{2} x \ln x-\frac{7}{4} x+C$ 
D)  $\frac{7}{2} x^{2} \ln x-\frac{x^{2}}{4}+C$

Question 20

Find the area of the shaded region.
-

Accepted Answer

A)  49 
B)  14 
C)  7 
D)  42 
A)  49 
B)  14 
C)  7 
D)  42

Find the area of the shaded region. -

Find the integral. - $\int\left(\frac{1}{x}+\frac{2}{x^{2}}+\frac{3}{x^{3}}\right) d x$

Evaluate. - $\int\left(4 t^{2}+4 t-5\right) d t$

Solve the problem. -Suppose that a velocity function is given by $v(t)=2 t^{4}$ . Find the position function $s(t)$ if $s(0)=7$ .

Solve the problem. -Assume that the rate of change of the population of a certain city is given by $\frac{d y}{d t}=6000 e^{.06 t}$ , where $y$ is the population at time $t$ , in years. The population was 100,000 in 1980 . Assume $t=0$ is 1980. Predict the population in 1985 .

Find the integral. - $\int(y-1)^{7} d y$

Find the integral. - $\int 8 e^{4 y} d y$

Approximate the area under the curve and above the $x$ -axis using $n$ rectangles. Let the height of each rectangle be given by the value of the function at the right side of the rectangle. - $f(x)=x^{2}-3 x+4$ from $x=1$ to $x=5 ; n=4$

Find the area bounded by the given curves. - $x=0, x=1, y=x^{2}+6, y=x^{2}+2$

Find the integral. - $\int\left(3 x+5 x^{-1}\right) d x$

Evaluate. - $\int 10^{2 x} d x$

Evaluate the definite integral. - $\int_{0}^{1} \frac{1}{13 x+4} d x$

Find the general solution of the differential equation. - $\frac{d y}{d x}=63 x^{2}-6 x$

Estimate the value of the quantity -The graph below shows the rate of natural gas usage (in therms per day) in one household for a 30 -day period. Estimate the total number of therms used during this period. Use left endpoints and rectangles with widths of 3 days.

Find the integral. - $\int \frac{x d x}{\left(7 x^{2}+3\right)^{5}}$

Find the integral. - $\int\left(7 x^{-4}-9 x^{-1}\right) d x$

Use integration by parts to find the integral. - $\int 7 x \ln x d x$

Find the area of the shaded region. -

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Exam 13: Integral Calculus

Find the area of the shaded region. -

Find the integral. - ∫(1x+2x2+3x3)dx\int\left(\frac{1}{x}+\frac{2}{x^{2}}+\frac{3}{x^{3}}\right) d x∫(x1​+x22​+x33​)dx

Evaluate. - ∫(4t2+4t−5)dt\int\left(4 t^{2}+4 t-5\right) d t∫(4t2+4t−5)dt

Solve the problem. -Suppose that a velocity function is given by v(t)=2t4v(t)=2 t^{4}v(t)=2t4 . Find the position function s(t)s(t)s(t) if s(0)=7s(0)=7s(0)=7 .

Find the integral. - ∫(y−1)7dy\int(y-1)^{7} d y∫(y−1)7dy

Find the integral. - ∫8e4ydy\int 8 e^{4 y} d y∫8e4ydy

Approximate the area under the curve and above the xxx -axis using nnn rectangles. Let the height of each rectangle be given by the value of the function at the right side of the rectangle. - f(x)=x2−3x+4f(x)=x^{2}-3 x+4f(x)=x2−3x+4 from x=1x=1x=1 to x=5;n=4x=5 ; n=4x=5;n=4

Find the area bounded by the given curves. - x=0,x=1,y=x2+6,y=x2+2x=0, x=1, y=x^{2}+6, y=x^{2}+2x=0,x=1,y=x2+6,y=x2+2

Find the integral. - ∫(3x+5x−1)dx\int\left(3 x+5 x^{-1}\right) d x∫(3x+5x−1)dx

Evaluate. - ∫102xdx\int 10^{2 x} d x∫102xdx

Evaluate the definite integral. - ∫01113x+4dx\int_{0}^{1} \frac{1}{13 x+4} d x∫01​13x+41​dx

Find the general solution of the differential equation. - dydx=63x2−6x\frac{d y}{d x}=63 x^{2}-6 xdxdy​=63x2−6x

Estimate the value of the quantity -The graph below shows the rate of natural gas usage (in therms per day) in one household for a 30 -day period. Estimate the total number of therms used during this period. Use left endpoints and rectangles with widths of 3 days.

Find the integral. - ∫xdx(7x2+3)5\int \frac{x d x}{\left(7 x^{2}+3\right)^{5}}∫(7x2+3)5xdx​

Find the integral. - ∫(7x−4−9x−1)dx\int\left(7 x^{-4}-9 x^{-1}\right) d x∫(7x−4−9x−1)dx

Use integration by parts to find the integral. - ∫7xln⁡xdx\int 7 x \ln x d x∫7xlnxdx

Find the area of the shaded region. -

Algebra and Equations

Graphs, Lines, and Inequalities

Functions and Graphs

Exponential and Logarithmic Functions

Mathematics of Finance

Systems of Linear Equations and Matrices

Linear Programming

Sets and Probability

Counting, Probability Distributions, and Further Topics in Probability

Introduction to Statistics

Differential Calculus

Applications of the Derivative

Multivariate Calculus

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Find the integral. - $\int\left(\frac{1}{x}+\frac{2}{x^{2}}+\frac{3}{x^{3}}\right) d x$

Evaluate. - $\int\left(4 t^{2}+4 t-5\right) d t$

Solve the problem. -Suppose that a velocity function is given by $v(t)=2 t^{4}$ . Find the position function $s(t)$ if $s(0)=7$ .

Find the integral. - $\int(y-1)^{7} d y$

Find the integral. - $\int 8 e^{4 y} d y$

Approximate the area under the curve and above the $x$ -axis using $n$ rectangles. Let the height of each rectangle be given by the value of the function at the right side of the rectangle. - $f(x)=x^{2}-3 x+4$ from $x=1$ to $x=5 ; n=4$

Find the area bounded by the given curves. - $x=0, x=1, y=x^{2}+6, y=x^{2}+2$

Find the integral. - $\int\left(3 x+5 x^{-1}\right) d x$

Evaluate. - $\int 10^{2 x} d x$

Evaluate the definite integral. - $\int_{0}^{1} \frac{1}{13 x+4} d x$

Find the general solution of the differential equation. - $\frac{d y}{d x}=63 x^{2}-6 x$

Find the integral. - $\int \frac{x d x}{\left(7 x^{2}+3\right)^{5}}$

Find the integral. - $\int\left(7 x^{-4}-9 x^{-1}\right) d x$

Use integration by parts to find the integral. - $\int 7 x \ln x d x$