Calculus

Write the integral in one variable to find the volume of the solid obtained by rotating the first-quadrant region bounded by y = 0.5x^2 and y = x about the line x = 5.

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  1. using shells,
    v = ∫[0,2] 2πrh dx
    where r = 5-x and h=x-0.5x^2

    or, using discs,
    v = ∫[0,2] π(R^2-r^2) dy
    where R=5-y and r=5-√(2y)

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