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

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(Created page with "<span class="exam">Divide the interval <math>[0,\pi]</math> into four subintervals of equal length <math>\frac{\pi}{4}</math> and compute the right-endpoint Riemann sum of <ma...")
 
 
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<span class="exam">Divide the interval <math>[0,\pi]</math> into four subintervals of equal length <math>\frac{\pi}{4}</math> and compute the right-endpoint Riemann sum of <math>y=\sin (x)</math>
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<span class="exam"> Let &nbsp;<math style="vertical-align: -5px">f(x)=1-x^2</math>.
  
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<span class="exam">(a) Compute the left-hand Riemann sum approximation of &nbsp;<math style="vertical-align: -14px">\int_0^3 f(x)~dx</math>&nbsp; with &nbsp;<math style="vertical-align: 0px">n=3</math>&nbsp; boxes.
  
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<span class="exam">(b) Compute the right-hand Riemann sum approximation of &nbsp;<math style="vertical-align: -14px">\int_0^3 f(x)~dx</math>&nbsp; with &nbsp;<math style="vertical-align: 0px">n=3</math>&nbsp; boxes.
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!Foundations: &nbsp;  
 
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'''Solution:'''
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<span class="exam">(c) Express &nbsp;<math style="vertical-align: -14px">\int_0^3 f(x)~dx</math>&nbsp; as a limit of right-hand Riemann sums (as in the definition of the definite integral). Do not evaluate the limit.
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!Step 2: &nbsp;
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[[009B Sample Midterm 1, Problem 1 Solution|'''<u>Solution</u>''']]
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!Final Answer: &nbsp;
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[[009B Sample Midterm 1, Problem 1 Detailed Solution|'''<u>Detailed Solution</u>''']]
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[[009B_Sample_Midterm_1|'''<u>Return to Sample Exam</u>''']]
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[[009B_Sample_Midterm_3|'''<u>Return to Sample Exam</u>''']]
 

Latest revision as of 15:42, 12 November 2017

Let  .

(a) Compute the left-hand Riemann sum approximation of    with    boxes.

(b) Compute the right-hand Riemann sum approximation of    with    boxes.

(c) Express    as a limit of right-hand Riemann sums (as in the definition of the definite integral). Do not evaluate the limit.

Solution


Detailed Solution


Return to Sample Exam

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