Find the volume?

Question

Find the volume generated when the area bounded by y=sinx and the x-axis on 0<=x<=pi is rotated about the x-axis.

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Answer 1 · 2018-06-20T17:23:07

#pi^2/2#

#V = int_0^pi A(x) * dx#

#V = int_0^pi pi y^2 * dx#

#V = pi int_0^pi (sin x)^2 * dx#

#cos 2x = cos^2 x - sin^2 x#
#1 = cos^2 x + sin^2 x#

#1 - cos 2x = 2 sin^2 x#

#V = pi int_0^pi dx/2 - pi int_0^pi (cos 2x) /2 * dx#

#u = 2x => du = 2 * dx#

#V = pi/2 (pi - 0) - pi/2 int_0^{2 pi} cos u * (du)/2#

#V = pi^2/2 - pi/4 (0 - 0)#