# Quick Question- Definite Integral of a Square Root

• Mar 30th 2011, 07:28 PM
bcahmel
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?
• Mar 30th 2011, 07:43 PM
TheEmptySet
Quote:

Originally Posted by bcahmel
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
• Mar 30th 2011, 07:44 PM
tonio
Quote:

Originally Posted by bcahmel
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
• Mar 30th 2011, 07:46 PM
bcahmel
ok, thanks! I keep forgetting that with substitutions and definite integrals it changes