Homework Help: Finding the area of a circle using integration

1. May 7, 2010

satxer

Let's say I have the equation for a circle but don't know how to calculate its radius. How could I use integration to find its area?

2. May 7, 2010

julian92

You can always get the radius from circle equations !!

However, all circle equations are integrated by trigonometric substitution
and it can also be done by integration by parts but that is a bit tricky!!

3. May 7, 2010

jack action

The area of a circle is a equal to the area of two half-circle.

The equation of a half-circle (assuming (y-b) is always positive and that you don't understand that r is the radius):

$$\left(x-a\right)^2+\left(y-b\right)^2=r^2$$

So the area of a circle is equal to: $$2\int_{-r-a}^{r-a}y_{(x)}dx$$

That's a complicated way, but I guess it can be done.