April 16th, 2017, 09:37 AM  #1 
Newbie Joined: Apr 2017 From: te Posts: 1 Thanks: 0  shell method question
Use shell method to express the volume of the solid obtained by rotating the region bounded by the curves x = √cos 8y pi/8≦y≦pi/8 , and x = 0 about the line x =4? no need to compute the integral  no idea to solve this when about the line x but not line y... Thank you Last edited by khen; April 16th, 2017 at 09:51 AM. 
April 16th, 2017, 09:59 AM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,518 Thanks: 1240 
shells w/r to $x$ ... $\displaystyle V = 2\pi \int_a^b r(x) \cdot f(x) \, dx$ $\displaystyle V = \dfrac{\pi}{2} \int_0^1 (1x)\left[\arccos(x^2)\right] \, dx$ washers w/r to $y$ ... $\displaystyle V = \pi \int_c^d [R(y)]^2  [r(y)]^2 \, dy$ $\displaystyle V = 2\pi \int_0^{\pi/16} 1  \left[1  \sqrt{\cos(8y)}\right]^2 \, dy$ fyi, symmetry of the rotated region used in both integrals 

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