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Math Help - Calculus: volumes of rotation

  1. #1
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    Calculus: volumes of rotation

    i need some help w/ this problem

    the region bounded by y=x^3, y=0, x=3. Is rotated about the line x=-1. What is the volume of the resulting solid?

    help would greatly be appreciated
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by bavery25 View Post
    i need some help w/ this problem

    the region bounded by y=x^3, y=0, x=3. Is rotated about the line x=-1. What is the volume of the resulting solid?

    help would greatly be appreciated
    Hint: use the shell method.

    can you tell what the radius and height are?
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  3. #3
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    Hello, bavery25!

    Did you make a sketch?


    The region bounded by \begin{Bmatrix}y\:=\:x^3 \\y\:=\:0 \\ x\:=\:3\end{Bmatrix} is rotated about the line x=-1

    What is the volume of the resulting solid?
    Code:
                  |
                  |          *
                  |
            :     |         *
            :     |        *|
            :     |      *::|
            :     |   *:::::|
        - - : - - * - - - - + - -
           -1     |         3
                  |

    Formula: . V \;=\;2\pi\int^b_a\text{(radius)(height)}\,dx

    So we have: . V \;=\;2\pi\int^3_0(x+1)(x^3)\,dx

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  4. #4
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    (1+x) is radius i think and height is (x^3)
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  5. #5
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    oops need to correct it its x=1 not x=3 sry
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by bavery25 View Post
    oops need to correct it its x=1 not x=3 sry
    no matter, just change the 3 in Soroban's post to a 1, the upper limit of the integral
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    yea i had that part but my professor has the answer as 7pi/6 and i cant get that so idk what im doing wrong
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by bavery25 View Post
    yea i had that part but my professor has the answer as 7pi/6 and i cant get that so idk what im doing wrong
    i don't get \frac {7 \pi}6 either. make sure there's not some other problem with the question
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  9. #9
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    nope thats the question with the problem so i guess he is wrong
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  10. #10
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    what did u get as the answer
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