Question 1

Evaluate.
-$\int \frac{28}{x^{2}} d x$

Accepted Answer

A)  $-28 x+C$ 
B)  $28 x+C$ 
C)  $-\frac{28}{x}+C$ 
D)  $\frac{28}{x}+C$ 
A)  $-28 x+C$ 
B)  $28 x+C$ 
C)  $-\frac{28}{x}+C$ 
D)  $\frac{28}{x}+C$ C

Question 2

Solve the problem.
-Find $C(x)$ if $C^{\prime}(x)=5 x^{2}-7 x+4$ and $C(6)=260$.

Accepted Answer

A)  $C(x)=\frac{5}{3} x^{3}-\frac{7}{2} x^{2}+4 x-260$ 
B)  $C(x)=\frac{5}{3} x^{3}-\frac{7}{2} x^{2}+4 x+2$ 
C)  $C(x)=\frac{5}{3} x^{3}-\frac{7}{2} x^{2}+4 x-2$ 
D)  $C(x)=\frac{5}{3} x^{3}-\frac{7}{2} x^{2}+4 x+260$ 
A)  $C(x)=\frac{5}{3} x^{3}-\frac{7}{2} x^{2}+4 x-260$ 
B)  $C(x)=\frac{5}{3} x^{3}-\frac{7}{2} x^{2}+4 x+2$ 
C)  $C(x)=\frac{5}{3} x^{3}-\frac{7}{2} x^{2}+4 x-2$ 
D)  $C(x)=\frac{5}{3} x^{3}-\frac{7}{2} x^{2}+4 x+260$ B

Question 3

Find the general solution of the differential equation.
-$\frac{d y}{d x}+2 y=21$

Accepted Answer

A)  $\frac{21}{2}+e^{2 x}+\mathrm{Me}^{-2 x}$ 
B)  $\frac{21}{5}+\mathrm{Me}^{2 x}$ 
C)  $21+\mathrm{Me}^{2 \mathrm{x}}$ 
D)  $\frac{21}{2}+\mathrm{Me}^{-2 x}$ 
A)  $\frac{21}{2}+e^{2 x}+\mathrm{Me}^{-2 x}$ 
B)  $\frac{21}{5}+\mathrm{Me}^{2 x}$ 
C)  $21+\mathrm{Me}^{2 \mathrm{x}}$ 
D)  $\frac{21}{2}+\mathrm{Me}^{-2 x}$ D

Question 4

Solve the problem.
-For a particular circuit, the current (in amperes) after time $t$ (in seconds) at a certain point $P$ is given by $i=0.005 t^{0.21}$. Find the charge (in coulombs) that passes point $P$ during the first second.

Accepted Answer

A)  $0.005 \mathrm{C}$ 
B)  $244 \mathrm{C}$ 
C)  $1.21 \mathrm{C}$ 
D)  $0.0041 \mathrm{C}$ 
A)  $0.005 \mathrm{C}$ 
B)  $244 \mathrm{C}$ 
C)  $1.21 \mathrm{C}$ 
D)  $0.0041 \mathrm{C}$

Question 5

Evaluate.
-$\int 15 x^{-8} d x$

Accepted Answer

A)  $-\frac{15}{7} x^{-7}+C$ 
B)  $\left(\frac{105}{\mathrm{x}}\right)^{7}+C$ 
C)  $\left(\frac{15}{7 x}\right)^{9}+C$ 
D)  $-120 x^{-9}+C$ 
A)  $-\frac{15}{7} x^{-7}+C$ 
B)  $\left(\frac{105}{\mathrm{x}}\right)^{7}+C$ 
C)  $\left(\frac{15}{7 x}\right)^{9}+C$ 
D)  $-120 x^{-9}+C$

Question 6

Find the area of the shaded region.
-

Accepted Answer

A)  18 
B)  45 
C)  27 
D)  36 
A)  18 
B)  45 
C)  27 
D)  36

Question 7

Evaluate.
-$\int(\sqrt{x}+\sqrt[3]{x}) d x$

Accepted Answer

A)  $2 \sqrt{x}+3 \sqrt[3]{x}+C$ 
B)  $2 \sqrt{x}+2 \sqrt[3]{x}+C$ 
C)  $\frac{2}{3} x^{3 / 2}+\frac{3}{4} x^{4 / 3}+$ C 
D)  $\frac{1}{2} x^{3 / 2}+\frac{2}{3} x^{4 / 3}+C$ 
A)  $2 \sqrt{x}+3 \sqrt[3]{x}+C$ 
B)  $2 \sqrt{x}+2 \sqrt[3]{x}+C$ 
C)  $\frac{2}{3} x^{3 / 2}+\frac{3}{4} x^{4 / 3}+$ C 
D)  $\frac{1}{2} x^{3 / 2}+\frac{2}{3} x^{4 / 3}+C$

Question 8

Find the integral.
-$\int \frac{19}{2+5 y} d y$

Accepted Answer

A)  $19 \ln |2+5 y|+C$ 
B)  $\frac{19}{5} \ln |2+5 y|+C$ 
C)  $18 \ln |2+5 y|+C$ 
D)  $\frac{18}{5} \ln |2+5 y|+C$ 
A)  $19 \ln |2+5 y|+C$ 
B)  $\frac{19}{5} \ln |2+5 y|+C$ 
C)  $18 \ln |2+5 y|+C$ 
D)  $\frac{18}{5} \ln |2+5 y|+C$

Question 9

Write the word or phrase that best completes each statement or answers thequestion.
-A student finds the integral $\int \frac{\mathrm{du}}{\mathrm{a}^{2}-\mathrm{u}^{2}}$ in a table. The student wishes to find $\int \frac{\mathrm{dx}}{8-\mathrm{x}^{2}}$. How can the student use the table?

Accepted Answer

Make @#LAT-DLM& and

Question 10

Find the area bounded by the given curves.
-$y=\ln x$ and $y=16-x^{2} ;[4,5]$

Accepted Answer

A)  5.169 
B)  5.835 
C)  7.835 
D)  16.926 
A)  5.169 
B)  5.835 
C)  7.835 
D)  16.926

Question 11

Find the integral.
-$\int \frac{3}{3 x+1} d x$

Accepted Answer

A)  $3 \ln |3 x+1|+C$ 
B)  $\ln (3 x+1)+C$ 
C)  $\ln |3 x+1|+C$ 
D)  $\frac{1}{3} \ln |3 x+1|+C$ 
A)  $3 \ln |3 x+1|+C$ 
B)  $\ln (3 x+1)+C$ 
C)  $\ln |3 x+1|+C$ 
D)  $\frac{1}{3} \ln |3 x+1|+C$

Question 12

Write the word or phrase that best completes each statement or answers thequestion.
-A student has supply and demand equations and needs to calculate the consumer's surplus. The student needs the equilibrium quantity to use the calculation. How can the student obtain this missing information?

Accepted Answer

Solve the demand and

Question 13

Find the general solution of the differential equation.
-$\frac{d y}{d x}=x-25$

Accepted Answer

A)  $\frac{x^{2}}{2}-25 x+C$ 
B)  $x^{3}-25 x+C$ 
C)  $\frac{x^{2}}{2}-x+C$ 
D)  $2 x^{2}-25+C$ 
A)  $\frac{x^{2}}{2}-25 x+C$ 
B)  $x^{3}-25 x+C$ 
C)  $\frac{x^{2}}{2}-x+C$ 
D)  $2 x^{2}-25+C$

Question 14

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

Accepted Answer

A)  0.78 
B)  0.86 
C)  0.68 
D)  0.96 
A)  0.78 
B)  0.86 
C)  0.68 
D)  0.96

Question 15

Find the integral.
-$\int\left(\frac{9}{x}-8 e^{-.7 x}\right) d x$

Accepted Answer

A)  $\frac{18}{x^{2}}-\frac{28}{5} e^{-.7 x}+C$ 
B)  $-\frac{9}{x^{2}}+\frac{28}{5} e^{-.7 x}+C$ 
C)  $9 \ln |x|-\frac{80}{7} e^{-.7 x}+C$ 
D)  $9 \ln |x|+\frac{80}{7} e^{-.7 x}+C$ 
A)  $\frac{18}{x^{2}}-\frac{28}{5} e^{-.7 x}+C$ 
B)  $-\frac{9}{x^{2}}+\frac{28}{5} e^{-.7 x}+C$ 
C)  $9 \ln |x|-\frac{80}{7} e^{-.7 x}+C$ 
D)  $9 \ln |x|+\frac{80}{7} e^{-.7 x}+C$

Question 16

Evaluate the definite integral.
-$\int_{1}^{3} \frac{8 x+11}{x} d x$

Accepted Answer

A)  $16+11 \ln 3$ 
B)  $8+11 \ln 3$ 
C)  $13+11 \ln 3$ 
D)  $11 \ln 3-3$ 
A)  $16+11 \ln 3$ 
B)  $8+11 \ln 3$ 
C)  $13+11 \ln 3$ 
D)  $11 \ln 3-3$

Question 17

Solve the problem.
-The rate at which an assembly line worker's efficiency $E$ (expressed as a percent) changes with respect to time $t$ is given by $E^{\prime}(t)=70-6 t$, where $t$ is the number of hours since the worker's shift began. Assuming that $\mathrm{E}(1)=92$, find $\mathrm{E}(\mathrm{t})$.

Accepted Answer

A)  $E(t)=70 t-3 t^{2}+92$ 
B)  $E(t)=70 t-6 t^{2}+25$ 
C)  $E(t)=70 t-3 t^{2}+25$ 
D)  $E(t)=70 t-3 t^{2}+159$ 
A)  $E(t)=70 t-3 t^{2}+92$ 
B)  $E(t)=70 t-6 t^{2}+25$ 
C)  $E(t)=70 t-3 t^{2}+25$ 
D)  $E(t)=70 t-3 t^{2}+159$

Question 18

Evaluate.
-$\int 12 x^{3} \sqrt{x} d x$

Accepted Answer

A)  $\frac{11}{5} x^{9 / 2}+C$ 
B)  $\frac{8}{3} x^{9 / 2}+C$ 
C)  $\frac{2}{9} x^{9 / 2}+C$ 
D)  $\frac{24}{7} x^{9 / 2}+C$ 
A)  $\frac{11}{5} x^{9 / 2}+C$ 
B)  $\frac{8}{3} x^{9 / 2}+C$ 
C)  $\frac{2}{9} x^{9 / 2}+C$ 
D)  $\frac{24}{7} x^{9 / 2}+C$

Question 19

Evaluate the definite integral.
-$\int_{0}^{1}\left(e^{9 x}-e^{-9 x}\right) d x$

Accepted Answer

A)  $\frac{1}{9} e^{9}+\frac{1}{9} e^{-9}$ 
B)  $\frac{1}{9} e^{9}+\frac{1}{9} e^{-9}-\frac{2}{9}$ 
C)  $\frac{1}{9} e^{9}+\frac{1}{9} e^{-9}-2$ 
D)  $\frac{1}{9} e^{9}-\frac{1}{9} e^{-9}$ 
A)  $\frac{1}{9} e^{9}+\frac{1}{9} e^{-9}$ 
B)  $\frac{1}{9} e^{9}+\frac{1}{9} e^{-9}-\frac{2}{9}$ 
C)  $\frac{1}{9} e^{9}+\frac{1}{9} e^{-9}-2$ 
D)  $\frac{1}{9} e^{9}-\frac{1}{9} e^{-9}$

Question 20

Solve the problem.
-Find the consumer's surplus if the demand function for an item is given by $D(x)=30-x^{2}$, assuming supply and demand are in equilibrium at $x=4$.

Accepted Answer

A)  $\frac{128}{3}$ 
B)  128 
C)  64 
D)  $\frac{64}{3}$ 
A)  $\frac{128}{3}$ 
B)  128 
C)  64 
D)  $\frac{64}{3}$

Evaluate. - $\int \frac{28}{x^{2}} d x$

Solve the problem. -Find $C(x)$ if $C^{\prime}(x)=5 x^{2}-7 x+4$ and $C(6)=260$ .

Find the general solution of the differential equation. - $\frac{d y}{d x}+2 y=21$

Solve the problem. -For a particular circuit, the current (in amperes) after time $t$ (in seconds) at a certain point $P$ is given by $i=0.005 t^{0.21}$ . Find the charge (in coulombs) that passes point $P$ during the first second.

Evaluate. - $\int 15 x^{-8} d x$

Find the area of the shaded region. -

Evaluate. - $\int(\sqrt{x}+\sqrt[3]{x}) d x$

Find the integral. - $\int \frac{19}{2+5 y} d y$

Write the word or phrase that best completes each statement or answers thequestion. -A student finds the integral $\int \frac{\mathrm{du}}{\mathrm{a}^{2}-\mathrm{u}^{2}}$ in a table. The student wishes to find $\int \frac{\mathrm{dx}}{8-\mathrm{x}^{2}}$ . How can the student use the table?

Find the area bounded by the given curves. - $y=\ln x$ and $y=16-x^{2} ;[4,5]$

Find the integral. - $\int \frac{3}{3 x+1} d x$

Write the word or phrase that best completes each statement or answers thequestion. -A student has supply and demand equations and needs to calculate the consumer's surplus. The student needs the equilibrium quantity to use the calculation. How can the student obtain this missing information?

Find the general solution of the differential equation. - $\frac{d y}{d x}=x-25$

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

Find the integral. - $\int\left(\frac{9}{x}-8 e^{-.7 x}\right) d x$

Evaluate the definite integral. - $\int_{1}^{3} \frac{8 x+11}{x} d x$

Evaluate. - $\int 12 x^{3} \sqrt{x} d x$

Evaluate the definite integral. - $\int_{0}^{1}\left(e^{9 x}-e^{-9 x}\right) d x$

Solve the problem. -Find the consumer's surplus if the demand function for an item is given by $D(x)=30-x^{2}$ , assuming supply and demand are in equilibrium at $x=4$ .

Algebra and Equations

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Exponential and Logarithmic Functions

Mathematics of Finance

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Counting, Probability Distributions, and Further Topics in Probability

Introduction to Statistics

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Exam 13: Integral Calculus

Evaluate. - ∫28x2dx\int \frac{28}{x^{2}} d x∫x228​dx

Solve the problem. -Find C(x)C(x)C(x) if C′(x)=5x2−7x+4C^{\prime}(x)=5 x^{2}-7 x+4C′(x)=5x2−7x+4 and C(6)=260C(6)=260C(6)=260 .

Find the general solution of the differential equation. - dydx+2y=21\frac{d y}{d x}+2 y=21dxdy​+2y=21

Solve the problem. -For a particular circuit, the current (in amperes) after time ttt (in seconds) at a certain point PPP is given by i=0.005t0.21i=0.005 t^{0.21}i=0.005t0.21 . Find the charge (in coulombs) that passes point PPP during the first second.

Evaluate. - ∫15x−8dx\int 15 x^{-8} d x∫15x−8dx