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Math Help - What is wrong with my Integration?

  1. #1
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    What is wrong (Integration)?Thanks,for help but is there a simpler/other way?

    The question is: Give an exakt value to P so that:
    P-sin^3v):dv = 1" alt="IntP-sin^3v):dv = 1" /> Int: limits are from 0->pi

     <br />
sin3v = 3sinv-4sin^3v -> 4sin^3v = 3sinv-sin3v -> sin^3v = 3/4sinv-1/4sin3v<br />

    Int(P-3/4sinv+1/4sin3v):dv from 0;pi
     <br /> <br />
Int(P-3/4sinv+1/4sin3v):dv<br />
= (Pv+3/4cosv-3/4cos3v)

    P(pi)+3/4+3/4-3/4-3/4 = 1 -> P(pi) = 1 but the answer is P = 7/3pi
    Last edited by Henryt999; January 14th 2010 at 01:21 PM. Reason: Maybe there is a simpler way?
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  2. #2
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    Sorry I did not follow your solution.
    Anyway, Here is the solution:
    \int_{0}^{\pi} ( P - sin^3(v) ) dv = 1
    P\int_{0}^{\pi} dv - \int_{0}^{\pi} sin^3(v) dv = 1
     (P)(\pi) - \int_{0}^{\pi} ( 1-cos^2(v) ) sin(v) dv = 1
    For the integral substitute
    <br />
t=cos(v)<br />
    <br />
dt=-sin(v) dv<br />
    <br />
t(\pi)=-1<br />
    <br />
t(0)=1<br />
    <br />
(P)(\pi) + \int_{1}^{-1} ( 1 - t^2 ) dt = 1<br />
    <br />
(P)(\pi) - \int_{-1}^{1} ( 1 - t^2 ) dt = 1<br />
    since f(t)=1-t^2 is an even function, the last equation can be writte as follows:
    <br />
(P)(\pi) - 2 \int_{0}^{1} ( 1 - t^2 ) dt = 1<br />
    Integrate and evaluate, to get:
    <br />
(P)(\pi) - 2 [ 1 - \frac{1}{3} ] = 1<br />
    <br />
(P)(\pi) - 2 (\frac{2}{3}) = 1<br />
    <br />
(P)(\pi) - \frac{4}{3} = 1<br />
    <br />
(P)(\pi) = \frac{7}{3}<br />
    <br />
P = (\frac{7}{3}) (\frac{1}{\pi})<br />
    <br />
P=\frac{7}{3\pi}<br />

    ----

    Use \pi to write pi`s symbol in LaTeX.
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  3. #3
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    Thanks

    Iīll give you Thanks for sure.

    But Oh My God is that what I have to do to solve it?
    Havenīt learned a thing about Integration by substitution yet, I checked the wikipedia for info on the subject, but I think it will take some time to melt. You wouldnīt happen to have a e-book/book to recommend on the subject? Or know anywhere I can find some info on how to integrate by substitution?
    Thanks you for your effort
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  4. #4
    Super Member General's Avatar
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    Quote Originally Posted by Henryt999 View Post
    Iīll give you Thanks for sure.

    But Oh My God is that what I have to do to solve it?
    Havenīt learned a thing about Integration by substitution yet, I checked the wikipedia for info on the subject, but I think it will take some time to melt. You wouldnīt happen to have a e-book/book to recommend on the subject? Or know anywhere I can find some info on how to integrate by substitution?
    Thanks you for your effort

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