JEE Main 2021 (Online) 25th February Morning ShiftQuestion 1
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 $\_\_\_\_\_\_$ .
Application of Integrals
Answer$64$
Solution
$\sin x=\cos x$ at $x=\frac\pi4,\frac{5\pi}4$ (consecutive). $A=\int_{\pi/4}^{5\pi/4}(\sin x-\cos x)dx=[-\cos x-\sin x]_{\pi/4}^{5\pi/4}=\sqrt2-(-\sqrt2)=2\sqrt2$. $A^4=(2\sqrt2)^4=64$.