1. ## [SOLVED] Trig Subst

Ok I know you have to do trig substitution but its been awhile since I've done so : /

The problem is : The integral of 2Sqrt(1-x^2)

Ok I know you have to do trig substitution but its been awhile since I've done so : /

The problem is : The integral of 2Sqrt(1-x^2)

I think if $\displaystyle \sqrt{a^2 -x^2}$ occurs in an integrand, you have to try the substitution $\displaystyle x=a sin \theta$. In this case a=1.

EDIT: I will show you one more step:

Since $\displaystyle x=a sin \theta$ implies that $\displaystyle \theta = sin^{-1} x$
Therefore, $\displaystyle dx = cos \theta d \theta$. Can you continue from here?

3. Originally Posted by Roam
Why would you want a trig substitution? Does re-writing it as $\displaystyle \int 2(1-x^2)^{\frac{1}{2}} dx$help?
I'm not sure what you have in mind but no, this doesn't help.

A trig substitution is required. One possible choice is $\displaystyle x = \sin t$.

@OP: If you need more help, please show all your working and say where it is that you get stuck.

4. The original posted question was wrong. See here: http://www.mathhelpforum.com/math-he...tml#post413788

This thread is being kept open in case other members want to follow up on the posted question.

5. Ok I'll brush up a bit on trig. subst.

6. ah ha! got it!

sin^-1(x) +(1 - x^2)^1/2 + c

The trick is to pull the 2 in front of the integral before you start and let x = sinx and go from there! ok thanks! : )