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Problem 22 Medium Difficulty

(a) Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curve about the specified axis.
(b) Use your calculator to evaluate the integral correct to five decimal places.

$ y = \tan x $ , $ y = 0 $ , $ x = \frac{\pi}{4} $ ; about $ x = \frac{\pi}{2} $

Answer

a) $V=2 \pi \int_{0}^{\pi / 4}\left(\frac{\pi}{2}-x\right) \tan x d x$
b) $V \approx 2.25323$

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Video Transcript

we know the formula for this is gonna be to pie, which is our constant sits on the outside from our bounds, which in this case are gonna be 02 pi over four is given in the problem of high over to cause we're rotating around pie over to and then we know it's gonna be subtracting. Thanks. Because remember, we have our two parts, which means it's gonna be multiplied by 10 of X d axe. So are integral is two pi times integral from zero to power for over two months. Acts times can of x t x. This is white complicated, Which is why part B of this is to use your calculator. If we plug this into the calculator directly into your tea I 84 plus calculator, you get 2.25 323