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Math Help - finding area and volume

  1. #1
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    finding area and volume

    the area enclosed between the curve y=e^x ,the x axis and the lines x=0 and x=2 is revolved about the x axis . find the volume swept out using intergration
    2
    i know that , PI ( ex^2 dx
    )
    0
    the promblem is with the e^x to the power 2 if i intergrate it do i have to treat it as 2 functions and if so how do i do that cause never done that in intergration only in differentation. ty for any help
    Last edited by mr fantastic; June 4th 2009 at 04:47 AM. Reason: Replaced ex with e^x
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  2. #2
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    Quote Originally Posted by alpharebel10 View Post
    the area enclosed between the curve y=e^x ,the x axis and the lines x=0 and x=2 is revolved about the x axis . find the volume swept out using intergration
    2
    i know that , PI ( ex^2 dx
    )
    0
    the promblem is with the e^x to the power 2 if i intergrate it do i have to treat it as 2 functions and if so how do i do that cause never done that in intergration only in differentation. ty for any help
    \left( e^x \right)^2 = e^{2x} NOT e^{x^2}.
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  3. #3
    MHF Contributor Amer's Avatar
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    \int_{0}^{2} (e^x)dx this is the area

    \pi\int_{0}^{2} (e^x)^2 dx this is the volume

    \pi\int_{0}^{2} (e^{2x}) dx

    try to lean latex it is easy

    thats what I write in latex but you should delete the 1 in the [1/math]
    then you will have the same as what I write

    [tex]\int_{0}^{2} (e^x)dx[1/math]

    [tex]\pi\int_{0}^{2} (e^x)^2 dx[1/math]

    [tex]\pi\int_{0}^{2} (e^{2x}) dx[1/math]
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  4. #4
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    Quote Originally Posted by Amer View Post
    \int_{0}^{2} (e^x)dx this is the area

    \pi\int_{0}^{2} (e^x)^2 dx this is the volume

    \pi\int_{0}^{2} (e^{2x}) dx

    try to lean latex it is easy

    thats what I write in latex but you should delete the 1 in the [1/math]
    then you will have the same as what I write

    [tex]\int_{0}^{2} (e^x)dx[1/math]

    [tex]\pi\int_{0}^{2} (e^x)^2 dx[1/math]

    [tex]\pi\int_{0}^{2} (e^{2x}) dx[1/math]
    thanks for your help but has the e^2x been intergrated or do i have to do that now then just plug the numbers in
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  5. #5
    MHF Contributor Amer's Avatar
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    no you have to integrate it you see the integrate symbol right
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