The area of the region bounded by the circle x2 + y2 = 1 is ______.

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KollegeApply · Accepted Answer

The area of the region bounded by the circle x2 + y2 = 1 is $\pi$ sq.units. Explanation: Given equation of circle is x2 + y2 = 1 $\Rightarrow$ y = sqrt(1 - x^2) Since the circle is symmetrical about the axes. $\therefore$ Required area = `4 xx int_0^1 sqrt(1 - x^2) "d"x = 4[x/2 sqrt(1 - x^2) + $\frac{1}{2}$ sin^-1 x]_0^1 = 4[0 + $\frac{1}{2}$ sin^-1 (1) - 0 - 0] = 4 xx $\frac{1}{2}$ xx pi/2` = $\pi$ sq.units [Solution diagram: 251756_solution_1.png]

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