JEE Main · 2021 · 25 Feb 2021 · Shift 1 · Area Under Curves

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The graphs of sine and cosine functions, intersect each other at a number of points and between two consecutive points of intersection, the two graphs enclose the same area

A

. Then

A^{4}

is equal to

Answer: 64

Solution

The graphs meet where

tan x = 1

, so two consecutive intersections are

x = \frac{π}{4}

and

x = \frac{5 π}{4}

, and between them

sin x > cos x

. The enclosed area is

A = \int_{π /4}^{5 π /4} (sin x - cos x) d x = [- cos x - sin x]_{π /4}^{5 π /4} = 2 - (- 2) = 22 .

Hence

A^{4} = (22)^{4} = 16 \times 4 = 64

JEE Main · 2021 · 25 Feb 2021 · Shift 1 · Integer answer

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