The graphs of sine and cosine functions,

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

Solution:

 

$

Required area

$=2 \int_{0}^{\sqrt{3}}\left(2 x^{2}+9-5 x^{2}\right) d x$

$=2 \int_{0}^{\sqrt{3}}\left(9-3 x^{2}\right) d x$

$=2\left|9 x-x^{3}\right|_{0}^{\sqrt{3}}=12 \sqrt{3}$

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