anonymous
  • anonymous
How to find the area of a circle by integration?
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
do you have an equation and what coordinates are you in?
anonymous
  • anonymous
say x^2 + y^2 = 1
dumbcow
  • dumbcow
\[Area = 2 \pi \int\limits_{0}^{R}r dr\] where R is radius of circle

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anonymous
  • anonymous
In doing so I am trying to find pi
dumbcow
  • dumbcow
haha prob not what you're looking for
dumbcow
  • dumbcow
\[x^{2} + y^{2} = 1\] \[y = \sqrt{1-x^{2}}\] this is top half of circle...integrate from -1 to 1 \[Area = 2\int\limits_{-1}^{1}\sqrt{1-x^{2}} dx = \pi\]
anonymous
  • anonymous
Yes, but how do i integrate \[\sqrt{1-x^2}\]
dumbcow
  • dumbcow
using trig substitution \[x = \sin u\] \[dx = \cos u\]
dumbcow
  • dumbcow
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
anonymous
  • anonymous
Yes, but why? And how come we can do that?
dumbcow
  • dumbcow
why can we use trig sub? you can substitute anything you want to make the integral more manageable

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