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Math Help - Volume of revolution help...

  1. #1
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    Volume of revolution help...

    The region bounded by the curve y = x^2 + 1, the x-axis, the y-axis and the line x = 2 is rotated completely about the x-axis. Find, in terms of \pi, the volume of the solid formed.

    Using x = 2, the lines should meet at y = 2^2 + 1 = 5. And the vertex is probably at 1, we have the integral limits of 1 and 5.

    Volume of the revolution is given by:
    \int_a^b \pi y^2 dy

    \int_1^5 \pi (y-1) dy = \pi [\frac{1}{2} y^2 - y]

    Using the above doesn't give me the correct answer, so I probably am not doing it right.
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  2. #2
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    Quote Originally Posted by struck View Post
    The region bounded by the curve y = x^2 + 1, the x-axis, the y-axis and the line x = 2 is rotated completely about the x-axis. Find, in terms of \pi, the volume of the solid formed.

    Using x = 2, the lines should meet at y = 2^2 + 1 = 5. And the vertex is probably at 1, we have the integral limits of 1 and 5.

    Volume of the revolution is given by:
    \int_a^b \pi y^2 dy

    \int_1^5 \pi (y-1) dy = \pi [\frac{1}{2} y^2 - y]

    Using the above doesn't give me the correct answer, so I probably am not doing it right.
    rotation about the x-axis using the disk method ...

    V = \pi \int_0^2 (x^2+1)^2 \, dx<br />
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