Answer
$\dfrac{\pi}{4}$
Work Step by Step
We rewrite as:
$I= \int_0^{\pi} \int_0^{\sin x} y dy dx$
or, $= \int_0^{\pi} [y^2/2]_0^{\sin x} dx $
Use formula: $ \sin ^2 x= \dfrac{1- \cos 2 x}{2}$
Now, $I=(1/4) \int_0^{\pi} 1-\cos 2x dx$
or, $=(1/4) [\pi -\dfrac{\sin 2 \pi}{2} ]$
So, $I=\dfrac{\pi}{4}$
