Answer
$2$
Work Step by Step
Consider $I=\int_{0}^{1} \int_{ 3 \sqrt y} \dfrac{2 \pi \sin (\pi x^2)}{x^2} \ dx \ dy$
or, $=\int_{0}^{1} \int_{0}^{x^3} \dfrac{2 \pi \sin (\pi x^2)}{x^2} \ dy \ dx$
or, $= \int_{0}^{1} 2 \pi x \sin (\pi x^2) \ dx$
or, $=[-\cos (\pi x^2) ]_0^1$
or, $=-(-1)-(-1)$
or, $=2$
