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| − | <span class="exam"> Otis Taylor plots the price per share of a stock that he owns as a function of time | + | <span class="exam">Evaluate the indefinite and definite integrals. |
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| − | <span class="exam">and finds that it can be approximated by the function | + | <span class="exam">(a) <math>\int x^2\sqrt{1+x^3}~dx</math> |
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| − | ::::::<math>s(t)=t(25-5t)+18</math>
| + | <span class="exam">(b) <math>\int _{\frac{\pi}{4}}^{\frac{\pi}{2}} \frac{\cos(x)}{\sin^2(x)}~dx</math> |
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| | + | [[009B Sample Midterm 1, Problem 2 Solution|'''<u>Solution</u>''']] |
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| − | <span class="exam">where <math>t</math> is the time (in years) since the stock was purchased.
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| − | <span class="exam">Find the average price of the stock over the first five years. | + | [[009B Sample Midterm 1, Problem 2 Detailed Solution|'''<u>Detailed Solution</u>''']] |
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| − | {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
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| − | !Foundations:
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| − | |The average value of a function <math style="vertical-align: -5px">f(x)</math> on an interval <math style="vertical-align: -5px">[a,b]</math> is given by <math style="vertical-align: -18px">f_{\text{avg}}=\frac{1}{b-a}\int_a^b f(x)~dx</math>.
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| − | '''Solution:'''
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| − | {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
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| − | !Step 1:
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| − | |Using the formula given in Foundations, we have:
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| − | | <math style="vertical-align: 0px">f_{\text{avg}}=</math>
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| − | {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
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| − | !Step 2:
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| − | {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
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| − | !Step 3:
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| − | {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
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| − | !Final Answer:
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| − | | <math></math>
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| | [[009B_Sample_Midterm_1|'''<u>Return to Sample Exam</u>''']] | | [[009B_Sample_Midterm_1|'''<u>Return to Sample Exam</u>''']] |
Evaluate the indefinite and definite integrals.
(a) 
(b) 
Solution
Detailed Solution
Return to Sample Exam