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Math Help - Integration by substitution

  1. #1
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    Question Integration by substitution

    Someone please help me! I don't get this problem...

    Use substitution to find: the integral from 0 to pi/3 of sinx/cos(squared)x dx
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  2. #2
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    Krizalid's Avatar
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    Put u=\cos x and don't forget the new bounds for u.
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  3. #3
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    Hello juicysharpie,

    iam just learning mathematics ,but i think i can answer this question

    let cos x = t

    differentiating this

    -sin x dx = dt

    so the numerator can be replaced by -dt and the denominator by tē.
    the limits are changed to t
    when x= 0,t becomes cos 0 and hence 1
    when x= pi/3 ,t becomes cos pi/3 and hence 1/2 .these are the limits of integration.
    hope you can do this from here.
    there are some very good mathematicians here ,but i just tried because i thought i could answer this.
    Last edited by kannan; February 3rd 2009 at 08:05 PM. Reason: sorry ,krizalid had already answered and i saw it only after i posted it
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  4. #4
    Senior Member mollymcf2009's Avatar
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    \int\limits_{0}^{\frac{\pi}{3}} \frac{sinx}{(cosx)^2} dx

    u = cos x

    du = - sinx dx

    -du = sinx dx

    The substitution gets rid of the sinx and dx in your integral which leaves you: ** don't forget to put that negative out in front of your integral!!

    - \int\limits_{0}^{\frac{\pi}{3}} \frac{1}{(u)^2} du

    You could plug cos x back in for u and solve using the same limits on your integral OR like Krizalid said you can integrate with the u in there and change your limits based on using u instead of cos x.

    If you are just learning to do u-substitution it might be better to plug cos x back in until you are comfortable with the concept of u-substitution.

    FYI, if you did want to change your limits so you could integrate leaving u in there all you do is plug your old limits into the "x" of your u = cos x equation. So

    u = cos (0) = 1 (would be your new lower limit)

    u = cos(\frac{\pi}{3} = \frac{1}{2} (would be your new upper limit)
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