Integral of sqrt(1-(x^2)) from -1 to 1

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jkb

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What is the integral of sqrt(1-(x^2)) from -1 to 1 ?

I know that this is an even function but i just cant solve this problem! I've tried by substitution and by parts and I either end up with an answer that makes no sense or an even harder equation :( Thanks for any help u can provide to help me solve this problem...im sure it'll probably end up being alot easier than i think!
 
Have you tried a trig substitution? Maybe x = sin(u)?
 
I've never learned trig substitution...could u explain it?
 
Look up 'trigonometric substitution' in your calc book. There should be an entire section for it.
 
jkb said:
I've never learned trig substitution...could u explain it?
Click to expand...
How are you supposed to do it? Have you ANY instructions? Is this a numerical methods class?

Note: In a rational academic environment, you CANNOT be given a problem with no indication of how to proceed.
 
You don't need any calculus to solve this question.

Consider: What does your function look like? If you aren't able to graph it yourself, find a graphing calculator or the internet.

You should see a familiar figure, and you should easily be able to evaluate this definite integral.

(remember... what does a definite integral mean?)
 
Nice, Chaotic. I completely overlooked that delightful simplification. Geometry has been around quite a bit longer than calculus.

In any case, jkb, you should have the tools before you are asked to use them. That should make sense to just about everyone.
 
tkhunny said:
Nice, Chaotic. I completely overlooked that delightful simplification. Geometry has been around quite a bit longer than calculus.

In any case, jkb, you should have the tools before you are asked to use them. That should make sense to just about everyone.
Click to expand...

=)
 
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