# Solution for this integral!

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

Is it possible to differentiate a root expression?

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

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

you could also evaluate the integral using a trig subsitution

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

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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.

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

AndersHermansson
Probably because it's a lot easier than you're used to. :)