Solution for this integral!

1. Jul 21, 2003

AndersHermansson

Is it possible to find an exact solution for this integral?

&int;&radic;(1-x*x)dx from 0 to 1

Is it possible to differentiate a root expression?

I found that:
pi = 4 * &int;&radic;(1-x*x)dx from 0 to 1

2. Jul 21, 2003

Suicidal

the equation is for a semicircle of radius 1 from 0 to 1 you get a quarter circle and 1/4 pi *r^2=1/4pi

1/4pi is the answer
you could also evaluate the integral using a trig subsitution

you already found the answer if you devide both sides of the equation by 4 in your solution you also get the answer

Last edited: Jul 21, 2003
3. Jul 21, 2003

Suicidal

for the trig sub

x=sin(&theta;)
dx=cos(&theta;)d&theta;
substitute into original integral simpligy trig expresion and switch limits of integration (evaluate interms of theta) and you will get &pi/4

if you haven't learned trig subs check it out in your calc book it not a very hard topic.

4. Jul 22, 2003

lethe

what is x*? is x a complex variable? i don t quite understand your integral

5. Jul 22, 2003

AndersHermansson

Probably because it's alot easier than you're used to. :)