Review IBP and Improper Integrals

Review IBP and Improper Integrals

11th - 12th Grade

13 Qs

quiz-placeholder

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Review IBP and Improper Integrals

Review IBP and Improper Integrals

Assessment

Quiz

Other

11th - 12th Grade

Medium

Created by

Kristin D'Emanuele

Used 54+ times

FREE Resource

13 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

What is the Integration by Parts Formula?

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2.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

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What would you choose for your u here if you used integration by parts?

t

3t

e2t

et

don't use IBP, let u = 2t

3.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Evaluate the indefinite integral using integration by parts. 
 3x e2x dx \int3x\ e^{2x}\ dx\   

 xe2x2+e2x4+C-\frac{xe^{2x}}{2}+\frac{e^{2x}}{4}+C  

 3xe2x23e2x4+C\frac{3xe^{2x}}{2}-\frac{3e^{2x}}{4}+C  

 xe2x+(1x2)2+Cxe^{-2x}+\frac{\left(1-x^2\right)^{ }}{2}+C  

 xe2x2+lne2x4+C-\frac{xe^{2x}}{2}+\frac{\ln e^{2x}}{4}+C  

4.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Evaluate the indefinite integral using integration by parts. u and  v' are provided.
 x4 lnx dx ;  u=lnx, v =x4\int x^{4\ }\ln x\ dx\ ;\ \ u=\ln x,\ v\ '=x^4  

 ex4x+4+C\frac{e^x}{4x+4}+C  

 2x32ln4x34x329+C\frac{2x^{\frac{3}{2}}\ln4x}{3}-\frac{4x^{\frac{3}{2}}}{9}+C  

 (4x21)e4x232+C\frac{\left(4x^2-1\right)\cdot e^{4x^2}}{32}+C  

 x5lnx5x525+C\frac{x^5\ln x}{5}-\frac{x^5}{25}+C  

5.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Evaluate the indefinite integral using integration by parts. u and v ' are provided.
 tsint dt ;   u=t, v =sint \int t\sin t\ dt\ ;\ \ \ u=t,\ v\ '=\sin t\   

 tcos1t(1t2)12+Ct\cos^{-1}t-\left(1-t^2\right)^{\frac{1}{2}}+C  

 tcost+sint+C-t\cos t+\sin t+C  

 tsin1t+(1t2)12+Ct\sin^{-1}t+\left(1-t^2\right)^{\frac{1}{2}}+C  

 tsint+cost+Ct\sin t+\cos t+C  

6.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

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What would you choose for your u here if you used integration by parts?

x

sin(x)

cos(x)

ex

7.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

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