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Math Help - Volume using Shell method. Stuck on last step!

  1. #1
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    Volume using Shell method. Stuck on last step!

    The volume of this solid can also be computed using cylindrical shells via an integral
    2pi(x+4)(4x-x^2) dx

    with limits of integration 0 and 4

    volume is cubic units.

    I am stuck on the last step. For some reason I tried integrating it and then plugging in the value, which in this case is just the beta, 4.

    What am I doing wrong? this is supposed to be easy step..
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  2. #2
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    Quote Originally Posted by softballchick View Post
    The volume of this solid can also be computed using cylindrical shells via an integral
    2pi(x+4)(4x-x^2) dx

    with limits of integration 0 and 4

    volume is cubic units.

    I am stuck on the last step. For some reason I tried integrating it and then plugging in the value, which in this case is just the beta, 4.

    What am I doing wrong? this is supposed to be easy step..
    I don't know ... you haven't shown any work.


    \displaystyle V = 2\pi \int_0^4 (x+4)(4x-x^2) \, dx

    expand the integrand and combine like terms ...

    \displaystyle V = 2\pi \int_0^4 16x - x^3 \, dx

    can you finish?
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  3. #3
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    Thanks!

    I am trying it on the other problems but got stuck on this one..

    integral of 2pi x^(1-6) from 0 to 7

    I got -1/4 x^4. I plugged in the 7 to get 2pi-(1/(4* 7^4)) but that's a negative volume? I took off the negative sign but still not right... thanks
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  4. #4
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    Quote Originally Posted by softballchick View Post
    Thanks!

    I am trying it on the other problems but got stuck on this one..

    integral of 2pi x^(1-6) from 0 to 7

    x^(1-6) = x^(-5) ... ???

    I got -1/4 x^4. I plugged in the 7 to get 2pi-(1/(4* 7^4)) but that's a negative volume? I took off the negative sign but still not right... thanks
    why don't you post the entire problem as written ... ?
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  5. #5
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    The volume of the solid obtained by rotating the region enclosed by

    y=1x 6y=0 x=1 x=7

    about the y-axis can be computed using the method of cylindrical shells via an integral
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  6. #6
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    Thanks, I figured it out! I made a dumb mistake, I took the integral from 0 to 7 instead of 1 to 7.
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