Finding the area of a circle using integration

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?

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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
Gold Member
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.