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The water level of a certain body of water is changing at a rate of $W(t)=\dfrac12\cos\left(3-\dfrac t2\right)$ inches per hour, where $t$ represents hours since $12$ a.m.

(A.) Write the integral that represents the number of inches that the water level changes from $6$ a.m. to noon.

(B.) What is the average daily number of inches that the water level changes for this lake?

(A.) So for this part, I'm pretty sure the integral would be $\displaystyle\int_6^{12}W(t)\,\mathrm dt$. Is this correct?

(B.) This is what I'm most confused about. Am I supposed to use average values, like maybe $$2\left[\frac 1{12-0}\int_0^{12}W(t)\right]\quad ?$$

an4s
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Ayanoria
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    What I understand from the question statement is that the rate $W(t)$ is representative of $24$ hours, i.e., from $12$ a.m. to $12$ a.m. of the next day. You should account for that in (B.). – an4s Aug 12 '20 at 17:04

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