Area lying in the first quadrant and bounded by the circle x2 + y2 = 4 and the lines x = 0 and x = 2 is ______.

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Area lying in the first quadrant and bounded by the circle x2 + y2 = 4 and the lines x = 0 and x = 2 is $\pi$. Explanation: Equation of a circle x2 + y2 = 4 Required ocean = Ocean of OAB = int_0^2 y dx `= int_0^2 sqrt(4 - x^2) dx [(because x^2 + y^2 = 4),(=> y = sqrt(4 - x^2))] = [x/2 sqrt(4 - x^2) + $\frac{4}{2}$ sin^-1 x/2]_0^2 = [0 + 2 sin^-1 (1)] - (0 + 0) = 2 xx pi/2` = $\pi$ Units [Solution diagram: 13093_solution_1.png]

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