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| − | <span class="exam"> The rate of reaction to a drug is given by: | + | <span class="exam"> Compute the following integrals: |
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| − | ::::::<math>r'(t)=2t^2e^{-t}</math>
| + | <span class="exam">(a) <math>\int x^2\sin (x^3) ~dx</math> |
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| − | <span class="exam">where <math>t</math> is the number of hours since the drug was administered. | + | <span class="exam">(b) <math>\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \cos^2(x)\sin (x)~dx</math> |
| | + | <hr> |
| | + | [[009B Sample Midterm 3, Problem 4 Solution|'''<u>Solution</u>''']] |
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| − | <span class="exam">Find the total reaction to the drug from <math>t=1</math> to <math>t=6.</math>
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| | + | [[009B Sample Midterm 3, Problem 4 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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| − | |If we calculate <math style="vertical-align: -14px">\int_a^b r'(t)~dt,</math> what are we calculating?
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| − | ::We are calculating <math style="vertical-align: -5px">r(b)-r(a).</math> This is the total reaction to the
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| − | ::drug from <math style="vertical-align: 0px">t=a</math> to <math style="vertical-align: 0px">t=b.</math>
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| − | '''Solution:'''
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| − | !Step 1:
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| − | !Step 2:
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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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| | [[009B_Sample_Midterm_3|'''<u>Return to Sample Exam</u>''']] | | [[009B_Sample_Midterm_3|'''<u>Return to Sample Exam</u>''']] |
Latest revision as of 18:30, 12 November 2017
Compute the following integrals:
(a) 
(b) 
Solution
Detailed Solution
Return to Sample Exam