The area of the region bounded by the y-axis, y = cosx and y = sinx, 0 $\leq$ x $\leq$ pi/2 is ______.

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The area of the region bounded by the y-axis, y = cosx and y = sinx, 0 $\leq$ x $\leq$ pi/2 is (sqrt(2) - 1) sq.units. Explanation: Given that y-axis, y = cos x, y = sin x, 0 $\leq$ x $\leq$ pi/2 Required area = `int_0^(pi/4) cos x "d"x - int_0^(pi/4) sin x "d"x = [sin x]_0^(pi/4) - [- cos x]_0^(pi/4) = [sin pi/4 - sin 0] + [cos pi/4 - cos 0] = [1/sqrt(2) - 0 + 1/sqrt(2) - 1] = 2/sqrt(2) - 1 = (sqrt(2) - 1)` sq.units [Solution diagram: 251704_solution_1.png]

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