Question

For a certain drug, the rate of reaction in appropriate units is given by R'(t)= 9/t + 2/t^2, where t is measured in hours after the drug is administered. Find the total reaction to the drug from t=2 to t=11. Round to two decimal places, if necessary. 

          For a certain drug,  the rate of reaction in appropriate units is given by R'(t)= 9/t + 2/t^2, where t is measured in hours after the drug is administered. Find the total reaction to the drug from t=2 to t=11. Round to two decimal places, if necessary.
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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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For a certain drug, the rate of reaction in appropriate units is given by R'(t)= 9/t + 2/t^2, where t is measured in hours after the drug is administered. Find the total reaction to the drug from t=2 to t=11. Round to two decimal places, if necessary.
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Transcript

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00:01 Okay, so for this problem, we're finding the rate of reaction for a given drug, and the equation we're given is r prime of t equals 9 over t plus 1 plus 2 over root t plus 1.
00:15 So to start off for part a, we're given from hour 1 to 8, and we're going to solve an integral of 9 over t plus 1 plus 2 over root t plus 1.
00:26 And taking the integral for that, we're going to get 9 ln, t plus 1, plus 4 times the square root of t plus 1 from 8 to 1.
00:37 Plugging in our values, we're going to get 9 ln9 plus 4 times the square root of 9 minus 9 times ln2 plus 4 times the square root of 2.
00:49 And that's going to give us 31 .775 minus 11 .895, which is going to equal 19 .88 for part a.
00:57 Then on to part b.
00:59 It's the same thing, but instead we're integrating for your different numbers...
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