Nepsesh Posted March 4, 2016 Share Posted March 4, 2016 (edited) Please help. My attempt to rotate the volume about the x-axis of y=x^2, first by disk method, then by shell method produces two answers - where obviously it should be the same answer. The limits are from 1 to 0. 1. V=Pi int(x^2)^2 dx = Pi int(y^4)dx = Pi/5 = 0.62631 ft cbd. (Disk method using f(x) where y=x^2). 2. V=2Pi int y.(sqrt y) dy = 4xPi/5 = 2.51327 ft cbd. (Shell method using g(y) where x=sq rt y). Couldn't be simpler? I've spent hours trying to see what's wrong. Edited March 4, 2016 by Nepsesh Link to comment Share on other sites More sharing options...
mathematic Posted March 5, 2016 Share Posted March 5, 2016 (edited) disc method: [latex]\pi \int_0^1 2x(1-x^2)dx[/latex] shell method: [latex]\pi \int_0^1 ydy[/latex] both methods give volume = [latex]\frac{\pi}{2}[/latex] Edited March 5, 2016 by mathematic Link to comment Share on other sites More sharing options...
Nepsesh Posted March 5, 2016 Author Share Posted March 5, 2016 Thanks so much for your answer, my error was in the (1-x^2) shell's 'height' assembly, ie missing the 1- from the limit. Much obliged, M. Link to comment Share on other sites More sharing options...
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