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Math Help - integration help

  1. #1
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    can someone please explain to me how to intergrate this:

    the definite integral from 0 to PI of (.25*PI) (1+kh) g (h + .2) dh

    I can leave g, PI, and k in the formula.

    -----------------------------------------------------------------------------------

    I was looking in my book at a similar problem. Here it is and it's answer:

    The definite integral from 0 to 1.5 of (.25 * PI) (1 + kh) g (h + 0.3) dh

    The answer: .366 (k + 1.077) gPI
    Last edited by mr fantastic; March 30th 2009 at 10:06 PM. Reason: Merged posts
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  2. #2
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    Quote Originally Posted by lauriecherie View Post
    can someone please explain to me how to intergrate this:

    the definite integral from 0 to PI of (.25*PI) (1+kh) g (h + .2) dh

    I can leave g, PI, and k in the formula.
    Your integral is \frac{g \pi}{4} \int_0^{\pi} (1 + kh)(h + 0.2) \, dh where k is a constant.

    Expand and integrate term-by-term:

    \frac{g \pi}{4} \int_0^{\pi} (1 + 0.2k) h + 0.2 + kh^2 \, dh

    = \frac{g \pi}{4} \left[ \frac{(1 + 0.2k)}{2} h^2 + 0.2 h + \frac{k}{3} h^3\right]_0^{\pi}

    = \frac{g \pi}{4} \left( \frac{(1 + 0.2k)}{2} \, \pi^2 + 0.2 \pi + \frac{k}{3} \pi^3\right).


    I've just noticed that in a later post you've changed the question. I'll let you make the appropriate changes in the above solution.
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