Find the area of the circle

Question

Find the area of the circle defined by the parametric equations $x = \cos t$ and $y = \sin t$.

I know this is circle defined by $x^2 +y^2 =1$ so i used $0 < t < 2\pi$ as my bounds, then integrated $\cos^2t$ and got my answer as $\pi$, this correct?

Answer 1

Write it as $$ A = \int_{0}^1\int_0^{2\pi} r\ {\rm d}\theta\ {\rm d}r = \pi. $$

Answer 2

Since $x^2 + y^2 = 1$ we see that the parameterized circle has radius $r = 1$, and consequently has area $\pi r^2 = \pi$.