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Math Help - Quick Question- Definite Integral of a Square Root

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    Quick Question- Definite Integral of a Square Root

    Say for example you wanted to find the integral of the square root of (x^2-1) on the interval 0 to 1.

    I know you would use a bunch of substitutions, but by the end would the interval still be 0 to 1? or does it change?
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    Quote Originally Posted by bcahmel View Post
    Say for example you wanted to find the integral of the square root of (x^2-1) on the interval 0 to 1.

    I know you would use a bunch of substitutions, but by the end would the interval still be 0 to 1? or does it change?
    It will usually change the limits of integration

    Integration by substitution - Wikipedia, the free encyclopedia
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    Quote Originally Posted by bcahmel View Post
    Say for example you wanted to find the integral of the square root of (x^2-1) on the interval 0 to 1.

    I know you would use a bunch of substitutions, but by the end would the interval still be 0 to 1? or does it change?


    Every substitution is bound to change the integration interval, so if you do a "bunch" of them then it's likely

    you'll end with a rather different int. interval...

    Now, in the very special case of your example \displaystyle{\int\limits^1_0\sqrt{x^2-1}\,dx , since the function in the integral

    is NOT defined within the integ. interval then the integral doesn't even exist, so

    you save yourself a bunch of substitutions and stuff.

    Tonio
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    ok, thanks! I keep forgetting that with substitutions and definite integrals it changes
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