Answer
$\approx 70.9963$
Work Step by Step
We have $z=x \sin y$
Surface area is given by:
$A(S)= \int_{-\pi}^{\pi}\int_{-3}^3 \sqrt {1+[\sin y]^2 +[x \cos y]^2} dx dy$
By using a calculator, we have
$A(S)= \int_{-\pi}^{\pi}\int_{-3}^3 \sqrt {1+\sin^2 y +x^2 \cos^2 y} dx dy \approx 70.9963$
