Question

show that the area of a circle x^2+y^2=a^2 is pi a^2

Answer 1

what is the radius of the circle : x^2 + y^2 = a^2 ??

Answer 2

solve for y
and get
y = sqrt(a^2-x^2) <- equation for a semi circle

integrate this from -a to a


once you integrate it you will get \[\Pi a^2 / 2 \]
since you found the area of a semicircle multiply it by 2 to get the area of the circle which is
\[\Pi a^2\]