Question 1

$\int_{-2}^{-1} \sin x^{2} d x>3$ .

Accepted Answer

A) True 
 B)False

Question 2

For any given function, TRAP(n)is always more accurate than LEFT(n).

Accepted Answer

A) True 
 B)False

Question 3

Integrate  ∫cos⁡23xsin⁡3xdx\int \cos ^{2} 3 x \sin 3 x d x∫cos23xsin3xdx  .

Accepted Answer

A)    cos⁡33x9+C\frac{\cos ^{3} 3 x}{9}+C9cos33x​+C 
B)    −cos⁡33x9+C-\frac{\cos ^{3} 3 x}{9}+C−9cos33x​+C 
C)    cos⁡33x3+C\frac{\cos ^{3} 3 x}{3}+C3cos33x​+C 
D)    −cos⁡33x27+C-\frac{\cos ^{3} 3 x}{27}+C−27cos33x​+C

Question 4

The table below shows the velocity v(t) of a falling object at various times (time t measured in seconds, velocity v(t) measured in meters per second) .  t012v(t) 172328\begin{array}{cccc}t & 0 & 1 & 2 \v(t)  & 17 & 23 & 28\end{array}tv(t) ​017​123​228​  The distance the object fell in these three seconds lies within which interval?

Accepted Answer

A)  (68, 75.5) 
B)  (75.5, 78) 
C)  (78, 83) 
D)  (83, 86.5)

Question 5

Is the area between $y=\frac{1}{x^{2}}$ and $y=\frac{1}{x^{5}}$ on (1, $\infty$)finite or infinite?

Accepted Answer

The answer of Is the area between $y=\frac{1}{x^{2}}$ and $y=\frac{1}{x^{5}}$...

Question 6

Evaluate the integral $\int_{a-2}^{a} \frac{d x}{(a-x)^{0.9}}$ to 3 decimal places, if it converges.If not, enter DNC.

Accepted Answer

The answer of Evaluate the integral $\int_{a-2}^{a} \frac{d x}{(a-x)^{0.9}}$ to...

Question 7

Consider the definite integral  ∫02/514+25x2dx\int_{0}^{2 / 5} \frac{1}{4+25 x^{2}} d x∫02/5​4+25x21​dx  .Compute the integral using the fundamental theorem of calculus and using the midpoint rule with n = 20.How far apart are your answers?

Accepted Answer

A)  Within 0.03 but not within 0.003
B)  Within 0.003 but not within 0.0003
C)  Within 0.0003 but not within 0.00003
D)  Within 0.00003 but not within 0.000003

Question 8

$\int \frac{7 x^{2}+6}{x^{2}+1} d x=7 x-\arctan x+C$ .

Accepted Answer

A) True 
 B)False

Question 9

Find  ∫5x4−x2dx\int \frac{5 x}{\sqrt{4-x^{2}}} d x∫4−x2​5x​dx

Accepted Answer

A)    −103(4−x2) 3/2+C-\frac{10}{3\left(4-x^{2}\right) ^{3 / 2}}+C−3(4−x2) 3/210​+C 
B)    103(4−x2) 3/2+C\frac{10}{3\left(4-x^{2}\right) ^{3 / 2}}+C3(4−x2) 3/210​+C 
C)    54−x2+C5 \sqrt{4-x^{2}}+C54−x2c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​+C 
D)    −54−x2+C-5 \sqrt{4-x^{2}}+C−54−x2c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​+C

Question 10

$\int\left(\sin ^{3} 2 \theta+5\right) \cos 2 \theta d \theta=\frac{1}{4} \sin ^{4} 2 \theta+\frac{5}{2} \sin 2 \theta+C$ .

Accepted Answer

A) True 
 B)False

Question 11

Evaluate exactly: $\int_{0}^{ x} x^{2} \sin x d x$ .(Leave $\pi$ in your answer.)

Accepted Answer

The answer of Evaluate exactly: \(\int_{0}^{ x} x^{2} \sin x...

Question 12

Show $\int \frac{1}{x^{2}+a^{2}} d x=\frac{1}{a} \arctan \frac{x}{a}+C$ by integrating the left hand side using the substitution $x=a \tan \theta$ .

Accepted Answer

If <img  loading="lazy" src="/assets/images/blured-textbook.svg" class="d-inline m-1" alt="blured image" width="139" height="30"> , then...

Question 13

Use the table of antiderivatives to determine if the following statement is true. $\int e^{7 x} \cos 8 x d x=\frac{1}{113} e^{7 x}(7 \cos 8 x+8 \sin 8 x)+C$

Accepted Answer

A) True 
 B)False

Question 14

Find  ∫3y(y2+2) 3dy\int 3 y\left(y^{2}+2\right) ^{3} d y∫3y(y2+2) 3dy

Accepted Answer

A)    38y(y2+2) 4+C\frac{3}{8 y}\left(y^{2}+2\right) ^{4}+C8y3​(y2+2) 4+C 
B)    3y28(y2+2) 4+C\frac{3 y^{2}}{8}\left(y^{2}+2\right) ^{4}+C83y2​(y2+2) 4+C 
C)    38(y2+2) 4+C\frac{3}{8}\left(y^{2}+2\right) ^{4}+C83​(y2+2) 4+C 
D)    34(y2+2) 4+C\frac{3}{4}\left(y^{2}+2\right) ^{4}+C43​(y2+2) 4+C

Question 15

$\int(x-1) e^{-x} d x=-x e^{-x}-e^{-x}+C$ .

Accepted Answer

A) True 
 B)False

Question 16

If $\int_{0}^{\infty} \frac{8}{\sqrt{1+x}} d x$ converges, find its value to 3 decimal places.Otherwise, enter "DNC".

Accepted Answer

The answer of If $\int_{0}^{\infty} \frac{8}{\sqrt{1+x}} d x$ converges, find...

Question 17

$\int \frac{7+x}{\sqrt{x}} d x=14 \sqrt{x}+\frac{2}{3} x^{\frac{3}{2}}+C$ .

Accepted Answer

A) True 
 B)False

Question 18

$\int_{0}^{3} \sin ^{39}(x) d x>\pi$ .

Accepted Answer

A) True 
 B)False

Question 19

$\int u^{-1} \ln u d u=(\ln u)^{2}+C$ .

Accepted Answer

A) True 
 B)False

Question 20

If $\int_{0}^{\infty} x^{2} e^{-x} d x$ converges, find its value.Otherwise, enter "DNC".

Accepted Answer

The answer of If $\int_{0}^{\infty} x^{2} e^{-x} d x$ converges,...

Exam 7: Integration

∫u−1ln⁡udu=(ln⁡u)2+C\int u^{-1} \ln u d u=(\ln u)^{2}+C∫u−1lnudu=(lnu)2+C .

Correct AnswerverifiedShow Answer

∫(sin⁡32θ+5)cos⁡2θdθ=14sin⁡42θ+52sin⁡2θ+C\int\left(\sin ^{3} 2 \theta+5\right) \cos 2 \theta d \theta=\frac{1}{4} \sin ^{4} 2 \theta+\frac{5}{2} \sin 2 \theta+C∫(sin32θ+5)cos2θdθ=41​sin42θ+25​sin2θ+C .

Correct AnswerverifiedShow Answer

∫7+xxdx=14x+23x32+C\int \frac{7+x}{\sqrt{x}} d x=14 \sqrt{x}+\frac{2}{3} x^{\frac{3}{2}}+C∫x​7+x​dx=14x​+32​x23​+C .

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Find ∫5x4−x2dx\int \frac{5 x}{\sqrt{4-x^{2}}} d x∫4−x2​5x​dx

Correct AnswerverifiedShow Answer

Evaluate exactly: ∫0xx2sin⁡xdx\int_{0}^{ x} x^{2} \sin x d x∫0x​x2sinxdx .(Leave π\piπ in your answer.)

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If ∫0∞x2e−xdx\int_{0}^{\infty} x^{2} e^{-x} d x∫0∞​x2e−xdx converges, find its value.Otherwise, enter "DNC".

Correct AnswerverifiedShow Answer

∫7x2+6x2+1dx=7x−arctan⁡x+C\int \frac{7 x^{2}+6}{x^{2}+1} d x=7 x-\arctan x+C∫x2+17x2+6​dx=7x−arctanx+C .

Correct AnswerverifiedShow Answer

Show ∫1x2+a2dx=1aarctan⁡xa+C\int \frac{1}{x^{2}+a^{2}} d x=\frac{1}{a} \arctan \frac{x}{a}+C∫x2+a21​dx=a1​arctanax​+C by integrating the left hand side using the substitution x=atan⁡θx=a \tan \thetax=atanθ .

Correct AnswerverifiedIf , then...View AnswerShow Answer

Evaluate the integral ∫a−2adx(a−x)0.9\int_{a-2}^{a} \frac{d x}{(a-x)^{0.9}}∫a−2a​(a−x)0.9dx​ to 3 decimal places, if it converges.If not, enter DNC.

Correct AnswerverifiedShow Answer

Integrate ∫cos⁡23xsin⁡3xdx\int \cos ^{2} 3 x \sin 3 x d x∫cos23xsin3xdx .

Correct AnswerverifiedShow Answer

Find ∫3y(y2+2) 3dy\int 3 y\left(y^{2}+2\right) ^{3} d y∫3y(y2+2) 3dy

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If ∫0∞81+xdx\int_{0}^{\infty} \frac{8}{\sqrt{1+x}} d x∫0∞​1+x​8​dx converges, find its value to 3 decimal places.Otherwise, enter "DNC".

Correct AnswerverifiedShow Answer

Is the area between y=1x2y=\frac{1}{x^{2}}y=x21​ and y=1x5y=\frac{1}{x^{5}}y=x51​ on (1, ∞\infty∞ )finite or infinite?

Correct AnswerverifiedShow Answer

∫−2−1sin⁡x2dx>3\int_{-2}^{-1} \sin x^{2} d x>3∫−2−1​sinx2dx>3 .

Correct AnswerverifiedShow Answer

Consider the definite integral ∫02/514+25x2dx\int_{0}^{2 / 5} \frac{1}{4+25 x^{2}} d x∫02/5​4+25x21​dx .Compute the integral using the fundamental theorem of calculus and using the midpoint rule with n = 20.How far apart are your answers?

Correct AnswerverifiedShow Answer

For any given function, TRAP(n)is always more accurate than LEFT(n).

Correct AnswerverifiedShow Answer

Use the table of antiderivatives to determine if the following statement is true. ∫e7xcos⁡8xdx=1113e7x(7cos⁡8x+8sin⁡8x)+C\int e^{7 x} \cos 8 x d x=\frac{1}{113} e^{7 x}(7 \cos 8 x+8 \sin 8 x)+C∫e7xcos8xdx=1131​e7x(7cos8x+8sin8x)+C

Correct AnswerverifiedShow Answer

∫03sin⁡39(x)dx>π\int_{0}^{3} \sin ^{39}(x) d x>\pi∫03​sin39(x)dx>π .

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∫(x−1)e−xdx=−xe−x−e−x+C\int(x-1) e^{-x} d x=-x e^{-x}-e^{-x}+C∫(x−1)e−xdx=−xe−x−e−x+C .

Correct AnswerverifiedShow Answer

$\int u^{-1} \ln u d u=(\ln u)^{2}+C$ .

Correct Answer
verified

$\int\left(\sin ^{3} 2 \theta+5\right) \cos 2 \theta d \theta=\frac{1}{4} \sin ^{4} 2 \theta+\frac{5}{2} \sin 2 \theta+C$ .

Correct Answer
verified

$\int \frac{7+x}{\sqrt{x}} d x=14 \sqrt{x}+\frac{2}{3} x^{\frac{3}{2}}+C$ .

Correct Answer
verified

Correct Answer
verified

Find $\int \frac{5 x}{\sqrt{4-x^{2}}} d x$

Correct Answer
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Evaluate exactly: $\int_{0}^{ x} x^{2} \sin x d x$ .(Leave $\pi$ in your answer.)

Correct Answer
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If $\int_{0}^{\infty} x^{2} e^{-x} d x$ converges, find its value.Otherwise, enter "DNC".

Correct Answer
verified

$\int \frac{7 x^{2}+6}{x^{2}+1} d x=7 x-\arctan x+C$ .

Correct Answer
verified

Show $\int \frac{1}{x^{2}+a^{2}} d x=\frac{1}{a} \arctan \frac{x}{a}+C$ by integrating the left hand side using the substitution $x=a \tan \theta$ .

Correct Answer
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If , then...
View Answer

Evaluate the integral $\int_{a-2}^{a} \frac{d x}{(a-x)^{0.9}}$ to 3 decimal places, if it converges.If not, enter DNC.

Correct Answer
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Integrate $\int \cos ^{2} 3 x \sin 3 x d x$ .

Correct Answer
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Find $\int 3 y\left(y^{2}+2\right) ^{3} d y$

Correct Answer
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If $\int_{0}^{\infty} \frac{8}{\sqrt{1+x}} d x$ converges, find its value to 3 decimal places.Otherwise, enter "DNC".

Correct Answer
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Is the area between $y=\frac{1}{x^{2}}$ and $y=\frac{1}{x^{5}}$ on (1, $\infty$ )finite or infinite?

Correct Answer
verified

$\int_{-2}^{-1} \sin x^{2} d x>3$ .

Correct Answer
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Consider the definite integral $\int_{0}^{2 / 5} \frac{1}{4+25 x^{2}} d x$ .Compute the integral using the fundamental theorem of calculus and using the midpoint rule with n = 20.How far apart are your answers?

Correct Answer
verified

Correct Answer
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Use the table of antiderivatives to determine if the following statement is true. $\int e^{7 x} \cos 8 x d x=\frac{1}{113} e^{7 x}(7 \cos 8 x+8 \sin 8 x)+C$

Correct Answer
verified

$\int_{0}^{3} \sin ^{39}(x) d x>\pi$ .

Correct Answer
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$\int(x-1) e^{-x} d x=-x e^{-x}-e^{-x}+C$ .

Correct Answer
verified