Difference between revisions of "009B Sample Midterm 2, Problem 1"

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<span class="exam">Consider the region <math>S</math> bounded by <math>x=1,x=5,y=\frac{1}{x^2}</math> and the <math>x</math>-axis.
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<span class="exam"> This problem has three parts:
  
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::<span class="exam">a) Use four rectangles and a Riemann sum to approximate the area of the region <math>S</math>. Sketch the region <math>S</math> and the rectangles and indicate your rectangles overestimate or underestimate the area of <math>S</math>.
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<span class="exam">(a) State the both parts of the fundamental theorem of calculus.
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::<span class="exam">b) Find an expression for the area of the region <math>S</math> as a limit. Do not evaluate the limit.
 
  
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<span class="exam">(b) Compute &nbsp; <math style="vertical-align: -15px">\frac{d}{dx}\int_0^{\cos (x)}\sin (t)~dt</math>.
  
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<span class="exam">(c) Evaluate &nbsp;<math style="vertical-align: -14px">\int_{0}^{\pi/4}\sec^2 x~dx</math>.
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!Foundations: &nbsp;
 
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|Answers:
 
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'''Solution:'''
 
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!Step 1: &nbsp;
 
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!Step 2: &nbsp;
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[[009B Sample Midterm 2, Problem 1 Solution|'''<u>Solution</u>''']]
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[[009B Sample Midterm 2, Problem 1 Detailed Solution|'''<u>Detailed Solution</u>''']]
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!Final Answer: &nbsp;
 
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[[009B_Sample_Midterm_2|'''<u>Return to Sample Exam</u>''']]
 
[[009B_Sample_Midterm_2|'''<u>Return to Sample Exam</u>''']]

Latest revision as of 17:58, 12 November 2017

This problem has three parts:

(a) State the both parts of the fundamental theorem of calculus.

(b) Compute   .

(c) Evaluate  .


Solution


Detailed Solution


Return to Sample Exam

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