# Thread: Integral of a quarter-circle

1. ## Integral of a quarter-circle

Find the area bounded by the curve y = (4-x^2)^1/2, the x-axis and the y-axis in the first quadrant.

I know what the integral is, but whenever I try to solve it I end up with 16/3 - when the answer should be pi units^2

Any help would be appreciated. Thanks.

3. ## Re: Integral of a quarter-circle

Originally Posted by HeroWise
Cheers!

4. ## Re: Integral of a quarter-circle

something that should be explicitly noted is that

$\sqrt{1-\sin^2 \theta} = |\cos \theta|$

(and in general, $\sqrt{x^2} = |x|$)

usually the bounds of the integral will mean that $|\cos \theta| = \cos \theta$ but one should still be careful when dealing with situations like this.

5. ## Re: Integral of a quarter-circle

Yes definetly, i have been in situations where i got that wrong lol. aka Weird vector questions which has both multiple positive cases and the negative cases which i missed because of that silly thing

6. ## Re: Integral of a quarter-circle

Originally Posted by fan96
something that should be explicitly noted is that

$\sqrt{1-\sin^2 \theta} = |\cos \theta|$

(and in general, $\sqrt{x^2} = |x|$)

usually the bounds of the integral will mean that $|\cos \theta| = \cos \theta$ but one should still be careful when dealing with situations like this.
Thank you.

On a completely unrelated note - how do you type in that font with the equations - I'm curious lol - it will make it 10 times easier next time I inevitably ask for help

7. ## Re: Integral of a quarter-circle

Originally Posted by Heresy
Thank you.

On a completely unrelated note - how do you type in that font with the equations - I'm curious lol - it will make it 10 times easier next time I inevitably ask for help
It's called tex.

Here is a good guide to get started: A Short Guide to LaTeX

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