Answer
$\sin (4)$
Work Step by Step
Consider $I=\int_{0}^{1} \int_{2y}^{2} 4 \cos x^2 \ dx \ dy$
or, $=\int_{0}^{2} \int_{0}^{x/2} 4 \cos x^2 \ dy \ dx$
or, $=\int_{0}^{2} 2x \cos x^2 \ dx$
or, $=[\sin x^2]_0^2$
or, $=\sin (2)^2-\sin 0$
or, $=\sin (4)$
