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Math Help - Intergrating function to power of 1/2

  1. #1
    RAz
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    Intergrating function to power of 1/2

    I'm having trouble integrating this arc length.

    General formula:

    L=\int{\sqrt{1+(f'(x))^2}} dx, between intervals a and b

    My function: y=ax^2-57, where a=0.00183

    So \frac{dy}{dx}=2ax

    Putting this derivative into general formula:

    L=\int{\sqrt{1+4a^2x^2}} dx, between the intervals of 176.3 and -176.3. (I haven't put a=0.00183 in yet because it would get too messy intergrating it.)

    I don't know how to integrate this because I think it involves some method of substitution which I don't know. Any help would be great ;D
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  2. #2
    Bop
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    If CAS are allowed:

    Function calculator
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  3. #3
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    Whenever you have 1+x^2 or 1-x^2 under the square root in an integral it would be a good idea to try some sort of trig substiution using either
    sin^2 +cos^2=1
    or
    cosh^2-sinh^2=1

    in this case of course you would use the hyperbolic identity.
    express 2ax=cosh(t)
    calculate the derivative and make the substitution.

    you should end up with
    (1/2a) int (sinh^2)

    express that in terms of e^x and its easy enough to integrate.
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