Finding the area of a circle using integration

[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?

 

[julian92]

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?

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!

 

[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.