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Problem 80 Hard Difficulty

A model for the basal metabolism rate, in kcal/h, of a young man is $ R(t) = 85 - 0.18 \cos(\pi t/12) $, where $ t $ is the time in hours measured from 5:00 AM. What is the total basal metabolism of this man, $ \displaystyle \int^{24}_0 R(t) \, dt $, over a 24-hour time period?

Answer

2040 $\mathrm{kcal}$

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Video Transcript

about this question. We are given that a model for the basal metabolic metabolic ism rate and kilocalories per are of a young man has given uh by the equation Artie uh Where t. Is the time? And ours measured from five a.m. What is a total basal metabolic um for this man? So we need to find integration with Artie The respective t. from 0 to 24. Uh so we are gonna do integration from 0 to 24 of 85 -0.18. Cause piety over 12. Uh d. T. So that's going to be equal to 85 DT integration. So we're just segregating opening of the parentheses minus 0.18 is a constant integration of course party over 12 DT again from 0 to 24. So this is just gonna be t. And then the limits are from 0-24. And this integration is gonna be a sign of party over 12. And we have 12 over pay as well because this is not just the this is party over 12. Uh So the integration gonna have this as well. Uh And this we have to place the limits from 0 to 24. Uh So over here we have 85 times 24 85 times 20 for -0.18. Now this is where we're gonna take 12 over pie outside. And now we're gonna use the calculator. So that's gonna be a sign of 20 for over 12 hours to pie. So and minus that's going to be zero Fortunately signed to buy a zero and 70 is also zero. So that's complete expression is just zero. So our answer is 85 times 24, which is going to be 20 for zero, which is the final answer because this is just zero. Uh, this is just zero. So we're going to say that the final answer is 2040. Thank you.