Let A 1 be the area of the region bounded by the curves y = sin x , y = cos x and y -axis in the first quadrant. Also, let A 2 be the area of the region bounded by the curves y = sin x , y = cos x , x -axis and x = π 2 in the first quadrant. Then,

Question

Let A 1 be the area of the region bounded by the curves y = sin x , y = cos x and y -axis in the first quadrant. Also, let A 2 be the area of the region bounded by the curves y = sin x , y = cos x , x -axis and x = π 2 in the first quadrant. Then,, 2 A 1 = A 2 and A 1 + A 2 = 1 + 2, A 1 : A 2 = 1 : 2 and A 1 + A 2 = 1, A 1 : A 2 = 1 : 2 and A 1 + A 2 = 1, A 1 = A 2 and A 1 + A 2 = 2

MARKS App · Accepted Answer

A 1 = ∫ 0 π / 4 cos x - sin x d x A 1 = sin x + cos x 0 π / 4 = 2 - 1 A 2 = ∫ 0 π / 4 sin x d x + ∫ π / 4 π / 2 cos x d x = - cos x 0 π / 4 + sin x π / 4 π / 2 A 2 = 1 - 1 2 + 1 - 1 2 = 2 - 2 A 1 : A 2 = 1 : 2 , A 1 + A 2 = 1

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