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Problem 25 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.

$ x = \sqrt{\sin y} $ , $ 0 \le y \le \pi $ , $ x = 0 $ ; about $ y = 4 $

Answer

a) $V=2 \pi \int_{0}^{\pi}(4-y) \sqrt{\sin y} d y$
b) $V \approx 36.57476$

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Video Transcript

we know we're gonna be plugging into the general formula to pi. Times integral from our bounds has given the problem there from zero to pie and are times h already ist is four minus y and our height is squirt of sign of why has given the problem times do you want? This is part is to write the integral part B is to use your calculator to solve if you put this into a graphing calculator or Wolfram outside, for example, or math way any sort of calculator You composed this indirectly, you got 36.5747 sex.