Difference between revisions of "009B Sample Midterm 3, Problem 3"

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!Foundations:    
 
!Foundations:    
 
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| u substitution
 
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!Step 1:    
 
!Step 1:    
 
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|-
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|We proceed using u substitution. Let <math>u=x^3</math>. Then, <math>du=3x^2dx</math>.
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|Therefore, we have
 
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|<math>\int x^2\sin (x^3) dx=\int \frac{\sin(u)}{3}du</math>
 
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!Step 2: &nbsp;
 
!Step 2: &nbsp;
 
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|We integrate to get
 
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|<math>\int x^2\sin (x^3) dx=\frac{-1}{3}\cos(u)+C=\frac{-1}{3}\cos(x^3)+C</math>
 
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!Final Answer: &nbsp;  
 
!Final Answer: &nbsp;  
 
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|'''(a)'''
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|'''(a)''' <math>\frac{-1}{3}\cos(x^3)+C</math>
 
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|'''(b)'''  
 
|'''(b)'''  
 
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[[009B_Sample_Midterm_3|'''<u>Return to Sample Exam</u>''']]
 
[[009B_Sample_Midterm_3|'''<u>Return to Sample Exam</u>''']]

Revision as of 12:38, 31 January 2016

Compute the following integrals:

a) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int x^2\sin (x^3) dx}
b)


Foundations:  
u substitution

Solution:

(a)

Step 1:  
We proceed using u substitution. Let Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle u=x^3} . Then, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle du=3x^2dx} .
Therefore, we have
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int x^2\sin (x^3) dx=\int \frac{\sin(u)}{3}du}
Step 2:  
We integrate to get
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \int x^2\sin (x^3) dx=\frac{-1}{3}\cos(u)+C=\frac{-1}{3}\cos(x^3)+C}

(b)

Step 1:  
Step 2:  
Final Answer:  
(a) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{-1}{3}\cos(x^3)+C}
(b)

Return to Sample Exam

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