Difference between revisions of "009B Sample Final 3, Problem 6"

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(Replaced content with "<span class="exam"> Find the following integrals <span class="exam">(a)  <math>\int \frac{3x-1}{2x^2-x}~dx</math> <span class="exam">(b)  <math>\int \frac{\sqr...")
 
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<span class="exam">(b) &nbsp;<math>\int \frac{\sqrt{x+1}}{x}~dx</math>
 
<span class="exam">(b) &nbsp;<math>\int \frac{\sqrt{x+1}}{x}~dx</math>
  
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!Foundations: &nbsp;
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[[009B Sample Final 3, Problem 6 Solution|'''<u>Solution</u>''']]
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|Through partial fraction decomposition, we can write the fraction
 
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|&nbsp; &nbsp; &nbsp; &nbsp;<math style="vertical-align: -18px">\frac{1}{(x+1)(x+2)}=\frac{A}{x+1}+\frac{B}{x+2}</math>
 
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|&nbsp; &nbsp; &nbsp; &nbsp;for some constants <math style="vertical-align: -4px">A,B.</math>
 
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'''Solution:'''
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[[009B Sample Final 3, Problem 6 Detailed Solution|'''<u>Detailed Solution</u>''']]
  
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!Step 1: &nbsp;
 
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|First, we factor the denominator to get
 
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|<math>\int \frac{3x-1}{2x^2-x}~dx=\int \frac{3x-1}{x(2x-1)}.</math>
 
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|We use the method of partial fraction decomposition.
 
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|We let
 
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|<math>\frac{3x-1}{x(2x-1)}=\frac{A}{x}+\frac{B}{2x-1}.</math>
 
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!Step 2: &nbsp;
 
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'''(b)'''
 
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!Step 1: &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_3|'''<u>Return to Sample Exam</u>''']]
 
[[009B_Sample_Final_3|'''<u>Return to Sample Exam</u>''']]

Latest revision as of 17:47, 2 December 2017

Find the following integrals

(a)  

(b)  

Solution


Detailed Solution


Return to Sample Exam

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