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First, recall that the formula for finding such a volume is pi times the integral from 0 to pi/2 of y^2 with respect to x. This leads to pi times the integral from 0 to pi/2 of 4sin^2(2x) + 4sin(2x) + 1 (...

First rewrite right hand side in terms of sinθ and cosθ, because those are the terms we'll be dealing with on the left hand side: sec2θ+tan2θ = 1/cos2θ + sin2θ/cos2θ, so RHS = (1+sin2θ)/cos2θNow look at t...

x = −b ± √(b² − 4ac) / 2a
x = −20 ± √(20² − 4(3)(-500)) / 2(3)
x = (3x + 50) (x - 10)