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Numerade Educator

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Problem 7 Medium Difficulty

Find the average value of the function on the given interval.

$ h(x) = \cos^4 x \sin x $ , $ [0, \pi] $

Answer

$h_{a v e}=\frac{2}{5 \pi}$

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Video Transcript

Okay. We know we're gonna be using the average value Formula one over B, which is pi minus. A witch is here from the bounds of a, which is zero to view just pie and then our function. Okay, now that we have this, what simplify our function? Remember that. Have used coastline X, then do you? Over DX is negative. Sign X. They're for Native do you is positive sign next. Yaks, which gives us negative you to the theft over five pie. And we know at this point we can reverse the boundaries to be from negative 1 to 1, cause we know we're gonna like either way, it works out. Just make sure that your subtracting from the biggest red is the smallest. Yeah, because in the end, we just end up the negatives. Cancel out. So we got one over five plus one over five pi, which gives us two over five ply