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Math Help - Integration Help.

  1. #1
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    Integration Help.

    Hi there

    I need some urgent help on a mathematical problem involving Integration.

    How do you integrate where -i = 25-x^2

    In other words how do you integrate twenty-five minus x squared, all square-rooted

    If you can do a step by step explanation, that'd really be appreciated, if not, still any help would be appreciated.

    Thanks
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by need2learn View Post
    Hi there

    I need some urgent help on a mathematical problem involving Integration.

    How do you integrate where -i = 25-x^2

    In other words how do you integrate twenty-five minus x squared, all square-rooted

    If you can do a step by step explanation, that'd really be appreciated, if not, still any help would be appreciated.

    Thanks
    integral sqrt(25 - x^2) dx.

    Change the variable, put x=5sin(u), then the integral becomes:

    integral 5 sqrt(1-sin^2(u)) 5 cos(u) du = integral 25 cos^2(u) du.

    Now use the identity cos^2(u) =(1/2) (1+cos(2u)) so now the integral becomes:

    integral 12.5 (1+cos(2u)) du = 12.5 [u + (1/2) sin(2u)]

    ...........................= 12.5 arcsin(x/5) + 12.5 sin(u)cos(u)

    ...........................= 12.5 arcsin(x/5) + 12.5 (x/5)sqrt(1-(x/5)^2)

    RonL
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  3. #3
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    Thanks CaptainBlack, I'll try and get some practise on it.
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