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

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

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Answer 1 · 2014-09-08T03:13:11

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#

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

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