Difference between revisions of "009B Sample Final 1, Problem 6"

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(Replaced content with "<span class="exam"> Evaluate the improper integrals: <span class="exam">(a)   <math>\int_0^{\infty} xe^{-x}~dx</math> <span class="exam">(b)   <math>\int_1^4 \...")
 
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<span class="exam"> Evaluate the improper integrals:
 
<span class="exam"> Evaluate the improper integrals:
  
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::<span class="exam">a) <math>\int_0^{\infty} xe^{-x}~dx</math>
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<span class="exam">(a) &nbsp; <math>\int_0^{\infty} xe^{-x}~dx</math>
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::<span class="exam">b) <math>\int_1^4 \frac{dx}{\sqrt{4-x}}</math>
 
  
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<span class="exam">(b) &nbsp; <math>\int_1^4 \frac{dx}{\sqrt{4-x}}</math>
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!Foundations: &nbsp;  
 
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|Review integration by parts
 
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'''Solution:'''
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<hr>
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[[009B Sample Final 1, Problem 6 Solution|'''<u>Solution</u>''']]
  
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'''(a)'''
 
  
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[[009B Sample Final 1, Problem 6 Detailed Solution|'''<u>Detailed Solution</u>''']]
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!Step 1: &nbsp;
 
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|First, we write <math>\int_0^{\infty} xe^{-x}~dx=\lim_{a\rightarrow \infty} \int_0^a xe^{-x}~dx</math>.
 
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|Now, we proceed using integration by parts. Let <math>u=x</math> and <math>dv=e^{-x}dx</math>. Then, <math>du=dx</math> and <math>v=-e^{-x}</math>.
 
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!Step 2: &nbsp;
 
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'''(b)'''
 
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!Step 1: &nbsp;
 
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!Step 2: &nbsp;
 
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!Step 3: &nbsp;
 
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!Final Answer: &nbsp;
 
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|'''(a)'''
 
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|'''(b)''' 
 
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[[009B_Sample_Final_1|'''<u>Return to Sample Exam</u>''']]
 
[[009B_Sample_Final_1|'''<u>Return to Sample Exam</u>''']]

Latest revision as of 17:19, 2 December 2017

Evaluate the improper integrals:

(a)  

(b)  

Solution


Detailed Solution


Return to Sample Exam

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