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Math Help - Volume of Revolution

  1. #1
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    Volume of Revolution

    I took these questions out of my book to review. I am stuck on volume of solids.

    Find the volume of the solid generated by revolving the shaded region around the x-axis.


    1.About the x axis
    y = 4 sec x







    2. y = (x)^.5, y = 0, x=0, x=6

    3. y= 1/x, y=0, x=1, x=5
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  2. #2
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    Quote Originally Posted by Collegeboy110 View Post
    I took these questions out of my book to review. I am stuck on volume of solids.

    Find the volume of the solid generated by revolving the shaded region around the x-axis.


    1.About the x axis
    y = 4 sec x







    2. y = (x)^.5, y = 0, x=0, x=6

    3. y= 1/x, y=0, x=1, x=5
    all three of these problems use the disk method ...

    general formula ... V = \pi \int_a^b [r(x)]^2 \, dx

    1. V = \pi \int_0^{\frac{\pi}{4}} (4\sec{x})^2 \, dx

    2. V= \pi \int_0^6 (\sqrt{x})^2 \, dx

    3. V = \pi \int_1^5 \left(\frac{1}{x}\right)^2 \, dx
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  3. #3
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    Thank you that was helpful. so when it says x=0, x=6.. you integrate it from 0 to 6?... the next step would be to integrate and that would be my answer?
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