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Math Help - Finding volume using the disc method

  1. #1
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    Finding volume using the disc method

     y=6-2x-x^{2}
    y=x+6

    Rotate around the x-axis.
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by yeloc View Post
     y=6-2x-x^{2}
    y=x+6

    Rotate around the x-axis.
    First find the points of intersection.

    They intersect when x+6=6-2x-x^2\implies x^2+3x=0\implies x(x+3)=0\implies x=0,-3.

    Thus, by the washers, you integral will take on the form of \pi\int_a^b\left(\left[f\!\left(x\right)\right]^2-\left[g\!\left(x\right)\right]^2\right)\,dx

    In this case f\!\left(x\right)=6-2x-x^2 and g\!\left(x\right)=x+6

    Thus, the volume of the solid about the x axis is \pi\int_{-3}^0\left(6-2x-x^2\right)^2-\left(x+6\right)^2\,dx=\pi\int_{-3}^0 x^4+4x^3-9x^2-36x\,dx

    Can you take it from here?
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  3. #3
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    Yes! Thanks!
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