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Q. Area of one loop formed by $ |y| = |\sin x| $ is

AMUAMU 2018

Solution:

We have, $|y|=|\sin x|$
The graph of given curve
image
The area of one loop
$=2 \int\limits_{0}^{\pi} \sin x d x $
$=2[-\cos x]_{0}^{\pi}=2[-\cos \pi+\cos 0]$
$=2(1+1)=4$