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> | |
− | <span class="exam"> | + | <span class="exam">a) Compute <math style="vertical-align: -15px">f(x)=\int_{-1}^{x} \sin(t^2)2tdt</math>. |
− | <span class="exam"> | + | <span class="exam">b) Find <math style="vertical-align: -5px">f'(x)</math>. |
− | <span class="exam">d) Use the | + | <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 style="vertical-align: -15px">\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;" |
Revision as of 12:36, 25 February 2016
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.
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Solution:
(a)
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(b)
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(c)
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(d)
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