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Question: The area bounded by the curves y = sin x, y = cos x and y-axis in first quadrant is –...

The area bounded by the curves y = sin x, y = cos x and y-axis in first quadrant is –

A

2\sqrt { 2 }–1

B

2\sqrt { 2 }

C

2\sqrt { 2 } +1

D

None of these

Answer

2\sqrt { 2 }–1

Explanation

Solution

In first quadrant sin x and cos x meet at x = p/4. The required area is a shown in the diagram. So required area

= 0π/4(cosxsinx)dx\int _ { 0 } ^ { \pi / 4 } ( \cos x - \sin x ) d x =

= (1/2\sqrt { 2 }+ 1/ 2\sqrt { 2 } ) – (0 + 1) = 2\sqrt { 2 } – 1