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TG3
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Homework Statement
Integrate the square root of (x^2 -1) over the interval 0-1.
The attempt at a solution
First off, I know this is a quarter of a circle, but I'm not supposed to solve it that way.
Now then:
x = sec theta
dx= sec tan theta.
square root (x^2-1) dx
becomes
square root (sec^2-1) sec tan
Square root (tan^2) sec tan
tan sec tan
sec tan^2
This is as far as I can get- I can't see any u substitutions that would work here, and don't know this integral off the top of my head either.
Integrate the square root of (x^2 -1) over the interval 0-1.
The attempt at a solution
First off, I know this is a quarter of a circle, but I'm not supposed to solve it that way.
Now then:
x = sec theta
dx= sec tan theta.
square root (x^2-1) dx
becomes
square root (sec^2-1) sec tan
Square root (tan^2) sec tan
tan sec tan
sec tan^2
This is as far as I can get- I can't see any u substitutions that would work here, and don't know this integral off the top of my head either.