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

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$\pi$ x2 + y2 = 4 represents a circle with centre at origin O(0, 0) and radius 2 units, cutting the coordinate axis at A, A', B and B'. x = 2 represents a straight line parallel to the y-axis, intersecting the circle at A(2, 0) x = 0 represents the y-axis Area bounded by the circle and the two given lines in the first quadrant is the shaded area OBCAO \text{ Area }\left( OBCAO \right) = \int_0^2 \left| y \right| dx = \int_0^2 $\sqrt$(4 - x^2) dx = \left[ $\frac{1}{2}$x$\sqrt$(4 - x^2) + $\frac{1}{2}$ $\times$ 4 \sin^{- 1} \left( x/2 \right) \right]_0^2 = $\frac{1}{2}$ $\times$ 2$\sqrt$(4 - 2^2) + $\frac{1}{2}$ $\times$ 4 \sin^{- 1} \left( $\frac{2}{2}$ \right) - 0 = 0 + 2 \sin^{- 1} \left( 1 \right) = 2 $\times$ $\pi$/2 = $\pi$\text{ sq units } [Solution diagram: 44147_solution_1.png]

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