- #1

- 60

- 0

∫√(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

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- Thread starter AndersHermansson
- Start date

- #1

- 60

- 0

∫√(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

- #2

- 22

- 1

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

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:

- #3

- 22

- 1

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.

- #4

- 653

- 0

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

- #5

- 60

- 0

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

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