Integral of sqrt(1-x^2)

I'm not sure if I've learned how to do this and forgotten, or if I never learned how, but I keep getting stuck on integrals involving square roots of polynomials. Can somebody give me a couple of pointers?

Question

Integral of sqrt(1-x^2)

I'm not sure if I've learned how to do this and forgotten, or if I never learned how, but I keep getting stuck on integrals involving square roots of polynomials. Can somebody give me a couple of pointers?

anonymous · Answer

trig sub. 1-x^2 is like a^2 - x^2 so let x=asin(theta) a=1

theoreo · Answer

Yeah, I was reading through my book and I think I tried it. 

If  $$\sqrt{1-x^2} ; a=1 $$

Then $$x = \sin(\theta)$$

so $$\sqrt{1-x^2} = \sqrt{1-\sin^2} = \sqrt{\cos^2}$$ right?

anonymous · Answer

yee

anonymous · Answer

then you just have the integral of cos(theta)

anonymous · Answer

but the most important thing is to turn your thetas back into x using a right triangle do you know that?

theoreo · Answer

Which is -sin(theta) right?

Ah I forgot the triangle. That's why I wasn't coming up with the right answer.

anonymous · Answer

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