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Problem 34 Hard Difficulty

Use a graph to estimate the x-coordinates of the points of intersection of the given curves. Then use this information and your calculator to estimate the volume of the solid obtained by rotating about the y-axis the region enclosed by these curves.

$ y = e^{\sin x} $ , $ y = x^2 - 4x + 5 $

Answer

$V \approx 21.2528$

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Video Transcript

using. Does most of your graphing calculator graphing the two functions? We end up with the shaded region like us and to intersection points 0.90 sex, comma 2.197 And then over here, we end up with 2.175 comma, 1.512 Okay, now that we have this, we know that we're gonna be slicing this way like this. And we know the our height is gonna be equivalent t e to the sign of axe minus X squared. Plus four acts months, five or radius is simply gonna be acts in this context, which means plugging into the general formula For volume, we are two pi times the integral from our two points, which are 0.9 of sex, 2.715 Again, this was all specified in the original side or radius is X height is e to the sign of axe minus X squared plus four acts minus five times D X. Using a calculator. If they said we get 21.25 to 8 is our solution