Math Calculus 1

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Have mercy!

Find the volume of the solid obtained by rotating y=3+2x-x^2, x+y=3 about the y-axis.

  • Math Calculus 1 -

    better integrate on x, since doing discs on y will need to separate the region into two pieces. So, using shells,

    v = ∫[0,3] 2πrh dx
    where r = x and h = (3+2x-x^2) - (3-x)
    v = 2π∫[0,3] x((3+2x-x^2) - (3-x)) dx
    = 2π∫[0,3] 3x^2-x^3 dx
    = 2π(x^3 - x^4/4) [0,3]
    = 27/2 π

  • Math Calculus 1 -

    Thank you!!!

  • Math Calculus 1 -

    If you would check my last 2 questions. I am just completely stumped.

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