## anonymous 3 years ago How to find the area of a circle by integration?

1. anonymous

do you have an equation and what coordinates are you in?

2. anonymous

say x^2 + y^2 = 1

3. anonymous

$Area = 2 \pi \int\limits_{0}^{R}r dr$ where R is radius of circle

4. anonymous

In doing so I am trying to find pi

5. anonymous

haha prob not what you're looking for

6. anonymous

$x^{2} + y^{2} = 1$ $y = \sqrt{1-x^{2}}$ this is top half of circle...integrate from -1 to 1 $Area = 2\int\limits_{-1}^{1}\sqrt{1-x^{2}} dx = \pi$

7. anonymous

Yes, but how do i integrate $\sqrt{1-x^2}$

8. anonymous

using trig substitution $x = \sin u$ $dx = \cos u$

9. anonymous

in the end you will just get pi =pi if you want to use this to get numerical approximation for pi, then integrate by computing area under curve using trapezoid rule or simpsons rule or something like that

10. anonymous

Yes, but why? And how come we can do that?

11. anonymous

why can we use trig sub? you can substitute anything you want to make the integral more manageable