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Integration with U Substitution

Authored by Dan Schwanekamp

Mathematics

11th Grade

CCSS covered

Used 119+ times

Integration with U Substitution
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24 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

∫5 e5x dx

25 e5x + C 
5 e5x - 1 + C 
e5x +  C 
(1/5) e5x + C 

Tags

CCSS.HSF.LE.A.1

2.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

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Tags

CCSS.HSF.TF.B.5

3.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

 ∫(3x−4)4dx\int\left(3x-4\right)^4dx  

 115(3x−4)5+C\frac{1}{15}\left(3x-4\right)^5+C  

 15(3x−4)5+C\frac{1}{5}\left(3x-4\right)^5+C  

 35(3x−4)5+C\frac{3}{5}\left(3x-4\right)^5+C  

 13(3x−4)5+C\frac{1}{3}\left(3x-4\right)^5+C  

4.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Using u=1+x2 u=1+x^{2\ } , rewrite the integral  ∫−13[x(1+x2)3]dx\int_{-1}^3\left[x\left(1+x^2\right)^3\right]dx  in terms of  uu  .

 12∫210u3du\frac{1}{2}\int_2^{10}u^3du  

 12∫−13u3du\frac{1}{2}\int_{-1}^3u^3du  

 ∫210u3du\int_2^{10}u^3du  

 2∫210u3du2\int_2^{10}u^3du  

Tags

CCSS.HSA.SSE.B.3

CCSS.HSA.SSE.A.2

5.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

 ∫ 1x+ 1x2 dx\int_{ }^{ }\ \frac{1}{x}+\ \frac{1}{x^2}\ dx  

 x−1 + x−2+ cx^{-1}\ +\ x^{-2}+\ c  

 x0 − x−1+ cx^0\ -\ x^{-1}+\ c  

 ln⁡x+ x−1+ c\ln x+\ x^{-1}+\ c  

 ln⁡x− x−1+ c\ln x-\ x^{-1}+\ c  

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

6.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

 ∫(x2−2x)dx\int\left(x^2-2x\right)dx  

 13x3−x2+C\frac{1}{3}x^3-x^2+C  

 x2 −2x+Cx^{2\ }-2x+C  

 2x−22x-2  

 13x3−x2\frac{1}{3}x^3-x^2 

Tags

CCSS.HSA.APR.A.1

7.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

 ∫(5x3−16e−4x+1x)dx\int\left(5\sqrt{x^3}-16e^{-4x}+\frac{1}{x}\right)dx  

 2x52+4x−4x+ln⁡∣x∣+C2x^{\frac{5}{2}}+4x^{-4x}+\ln\left|x\right|+C  

 5x13−4e−4x+1+C5x^{\frac{1}{3}}-4e^{-4x}+1+C  

 52x32−16e−4x+ln⁡∣x∣+C\frac{5}{2}x^{\frac{3}{2}}-16e^{-4x}+\ln\left|x\right|+C  

Got lazy with fake answers

Tags

CCSS.HSF.BF.B.5

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