# How do you find the area of circle using integrals in calculus?

By using polar coordinates, the area of a circle centered at the origin with radius ##R## can be expressed:
##A=int_0^{2pi}int_0^R rdrd theta=piR^2##

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Let us evaluate the integral,
##A=int_0^{2pi}int_0^R rdrd theta##
by evaluating the inner integral,
##=int_0^{2pi}[{r^2}/2]_0^R d theta=int_0^{2pi}R^2/2 d theta##
by kicking the constant ##R^2/2## out of the integral,
##R^2/2int_0^{2pi} d theta=R^2/2[theta]_0^{2pi}=R^2/2 cdot 2pi=piR^2##

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