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Find the area enclosed by the circle x^...

Find the area enclosed by the circle `x^2+y^2=a^2`.

Text Solution

Verified by Experts

Given equation of circle is:
`x^2+y^2=a^2`
`y^2 = a^2-x^2`
=> `y = sqrt(a^2-x^2)`
Area of circle = `4 xx` area of first quadrant
= `4int _0^a ydx`
= `4int _0^a sqrt(a^2-x^2)dx`
= `4[ x/(2) sqrt(a^2-x^2) + a^2/(2) sin^-1(x/a)]_0^a`
= `4[ a^2/(2) sin^-1 -0]` = `2a^2 . pi/2 = pia^2` square unit
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