Question

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 1

$A=\int\limits_{\pi / 4}^{5 \pi / 4}(\sin x-\cos x) d x$
$=\left.(-\cos x-\sin x)\right|_{\pi / 4} ^{5 \pi / 4}$
$=\left(-\left(\frac{-1}{\sqrt{2}}\right)-\left(\frac{-1}{\sqrt{2}}\right)\right)-\left(-\left(\frac{1}{\sqrt{2}}\right)-\left(\frac{1}{\sqrt{2}}\right)\right)$
$\Rightarrow A=\frac{2}{\sqrt{2}}+\frac{2}{\sqrt{2}}=2 \sqrt{2}$
$\Rightarrow A^{4}=(2 \sqrt{2})^{4}=16 \times 4=64$