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

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<span class="exam"> We would like to evaluate
 
<span class="exam"> We would like to evaluate
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:::::<math>\frac{d}{dx}\bigg(\int_{-1}^{x} \sin(t^2)2tdt\bigg)</math>.
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::<math>\frac{d}{dx}\bigg(\int_{-1}^{x} \sin(t^2)2t\,dt\bigg).</math>
  
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<span class="exam">a) Compute <math>f(x)=\int_{-1}^{x} \sin(t^2)2tdt</math>.
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<span class="exam">(a) Compute &nbsp;<math style="vertical-align: -15px">f(x)=\int_{-1}^{x} \sin(t^2)2t\,dt.</math>
  
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<span class="exam">b) Find <math>f'(x)</math>.
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<span class="exam">(b) Find &nbsp;<math style="vertical-align: -5px">f'(x).</math>
  
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<span class="exam">c) State the fundamental theorem of calculus.
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<span class="exam">(c) State the Fundamental Theorem of Calculus.
  
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<span class="exam">d) Use the fundamental theorem of calculus to compute <math>\frac{d}{dx}\bigg(\int_{-1}^{x} \sin(t^2)2tdt\bigg)</math> without first computing the integral.
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<span class="exam">(d) Use the Fundamental Theorem of Calculus to compute &nbsp;<math style="vertical-align: -15px">\frac{d}{dx}\bigg(\int_{-1}^{x} \sin(t^2)2t\,dt\bigg)</math>&nbsp; without first computing the integral.
  
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!Foundations: &nbsp;
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[[009B Sample Final 1, Problem 2 Solution|'''<u>Solution</u>''']]
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'''Solution:'''
 
  
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'''(a)'''
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[[009B Sample Final 1, Problem 2 Detailed Solution|'''<u>Detailed Solution</u>''']]
  
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!Final Answer: &nbsp;
 
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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 17:15, 2 December 2017

We would like to evaluate

(a) Compute  

(b) Find  

(c) State the Fundamental Theorem of Calculus.

(d) Use the Fundamental Theorem of Calculus to compute    without first computing the integral.

Solution


Detailed Solution


Return to Sample Exam

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