AP Calculus

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I need help with Volume of Revolutions. The question is: Find the volume of the solid generated bt rotating about the designated line the region bounded by:
1. y= x squared + 2, x = negative 1, x = 1 about y = 1.

  • AP Calculus -

    you will get the same solid if you rotate y = x^2 + 1 about the x-axis.

    then volume
    = [integral] pi(y^2)dx from -1 to 1
    or
    = 2pi[integral](x^2+1)^2 dx from 0 to 1
    = 2pi[integral](x^4 + 2x^2 + 1) dx from 0 to 1

    = ...
    this is quite easy to integrate and finish.

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