Difference between revisions of "009B Sample Final 2, Problem 7"

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<span class="exam">Evaluate the following integrals or show that they are divergent:
 
<span class="exam">Evaluate the following integrals or show that they are divergent:
  
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<span class="exam">(a) <math>\int_1^\infty \frac{\ln x}{x^4}~dx</math>
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<span class="exam">(a) &nbsp;<math>\int_1^\infty \frac{\ln x}{x^4}~dx</math>
  
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<span class="exam">(b) <math> \int_0^1 \frac{3\ln x}{\sqrt{x}}~dx</math>
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<span class="exam">(b) &nbsp;<math> \int_0^1 \frac{3\ln x}{\sqrt{x}}~dx</math>
  
 
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{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
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'''(b)'''
 
'''(b)'''
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!Step 1: &nbsp;
 
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!Step 2: &nbsp;
 
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'''(c)'''
 
  
 
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{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
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|'''(b)'''  
 
|'''(b)'''  
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|'''(c)'''
 
 
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[[009B_Sample_Final_2|'''<u>Return to Sample Exam</u>''']]
 
[[009B_Sample_Final_2|'''<u>Return to Sample Exam</u>''']]

Revision as of 12:51, 3 March 2017

Evaluate the following integrals or show that they are divergent:

(a)  

(b)  

Foundations:  


Solution:

(a)

Step 1:  
Step 2:  

(b)

Step 1:  
Step 2:  


Final Answer:  
(a)
(b)

Return to Sample Exam

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