Can the value of pi be found through integration?

[AndersHermansson]

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

∫√(1-x*x)dx from 0 to 1

Is it possible to differentiate a root expression?

I found that:
pi = 4 * ∫√(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

1/4pi is the answer
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

 

[Suicidal]

for the trig sub

x=sin(θ)
dx=cos(θ)dθ
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. :)