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
 
:::::<math>\frac{d}{dx}\bigg(\int_{-1}^{x} \sin(t^2)2tdt\bigg)</math>.
 
:::::<math>\frac{d}{dx}\bigg(\int_{-1}^{x} \sin(t^2)2tdt\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">b) Find <math>f'(x)</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">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">b) Find <math>f'(x)</math>.
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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.
  
 
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
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'''(c)'''
 
'''(c)'''
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{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
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!Step 1: &nbsp;
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{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
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!Step 2: &nbsp;
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|-
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'''(d)'''
  
 
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
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|'''(b)'''  
 
|'''(b)'''  
 
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|'''(c)'''  
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|'''(c)'''
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|-
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|'''(d)'''  
 
|}
 
|}
 
[[009B_Sample_Final_1|'''<u>Return to Sample Exam</u>''']]
 
[[009B_Sample_Final_1|'''<u>Return to Sample Exam</u>''']]

Revision as of 21:12, 1 February 2016

We would like to evaluate

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{d}{dx}\bigg(\int_{-1}^{x} \sin(t^2)2tdt\bigg)} .

a) Compute Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x)=\int_{-1}^{x} \sin(t^2)2tdt} .

b) Find Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f'(x)} .

c) State the fundamental theorem of calculus.

d) Use the fundamental theorem of calculus to compute Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{d}{dx}\bigg(\int_{-1}^{x} \sin(t^2)2tdt\bigg)} without first computing the integral.

Foundations:  

Solution:

(a)

Step 1:  
Step 2:  

(b)

Step 1:  
Step 2:  
Step 3:  

(c)

Step 1:  
Step 2:  

(d)

Step 1:  
Step 2:  
Final Answer:  
(a)
(b)
(c)
(d)

Return to Sample Exam

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