(Solution) - 1 Set up an integral for the volume of the -(2025 Original AI-Free Solution)

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Academic Level: Undergrad. (yrs 3-4)

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(1) Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curve about the specified axis.
(2) Use your calculator to evaluate the integral correct to five decimal places.
(a) y = xe-x, y = 0, x = 2; about the y-axis
(b) y = cos4x, y = - cos4x, - ?/2 ? x ? ?/2; about x = ?
(c) x = ?sin y, 0 ? y ? ?, x = 0; about y = 4