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?
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
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 $\displaystyle \displaystyle{\int\limits^1_0\sqrt{x^2-1}\,dx$ , 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