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Math Help - rotational volume question

  1. #1
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    rotational volume question

    Hi all, here's my question:

    Find the volume of the solid formed by rotating the region enclosed by
    y=e^(2x) + 1, y=0, x=0, x=0.2
    about the y-axis.

    My attempt at a solution:
    V = pi int{ x = 0 to 0.2} [ (e^(2x) + 1)^2 dx]
    V= pi int{ x = 0 to 0.2} [ ( e^(4x) + 2 e^(2x) + 1) dx]
    V= pi { x = 0 to 0.2} ( (1/4) e^(4x) + (2/2) e^(2x) + x)
    V = pi ( [(1/4) e^(0.8) + e^(0.4) + 0.4] - [(1/4) + 1] )

    This isn't the right answer though. I'd like to know what I did wrong so I can get credit here and do problems right in the future. Thanks!!!!!
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  2. #2
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    Quote Originally Posted by yeshtikvah View Post
    Hi all, here's my question:

    Find the volume of the solid formed by rotating the region enclosed by
    y=e^(2x) + 1, y=0, x=0, x=0.2
    about the y-axis.

    My attempt at a solution:
    V = pi int{ x = 0 to 0.2} [ (e^(2x) + 1)^2 dx]
    V= pi int{ x = 0 to 0.2} [ ( e^(4x) + 2 e^(2x) + 1) dx]
    V= pi { x = 0 to 0.2} ( (1/4) e^(4x) + (2/2) e^(2x) + x)
    V = pi ( [(1/4) e^(0.8) + e^(0.4) + 0.4] - [(1/4) + 1] )

    This isn't the right answer though. I'd like to know what I did wrong so I can get credit here and do problems right in the future. Thanks!!!!!

    All is correct but the last, usually easier, part of evaluation: it must be \frac{1}{4}e^{0.8}+e^{0.4}+0.2 <<<=== you put 0.4 instead...that's all the problem!

    Tonio
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  3. #3
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    Thank you!

    Yes, you're right that should have been .2!

    I tried that answer, but the online homework still says it's wrong.

    This happened with another problem I KNOW i did right. At least I know I'm doing the problems the right way. I guess I'll have to see my teacher to see why our answers aren't giving me any darn credit.
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  4. #4
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    Quote Originally Posted by yeshtikvah View Post
    Yes, you're right that should have been .2!

    I tried that answer, but the online homework still says it's wrong.

    This happened with another problem I KNOW i did right. At least I know I'm doing the problems the right way. I guess I'll have to see my teacher to see why our answers aren't giving me any darn credit.
    I don't know where some of you guys study that you've to produce your homework ONLINE and/or check it with some online checker or whatever.
    Anyway, check your result with a calculator..

    Tonio

    Ps. Im yesh tikvah az lo hakol avud...
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