Question

Evaluate the double-integral of sin(y^3) , where R is the region bounded by y=sqrt(x) , y=2 , and x=0 .

Answer 1

Your region \(R\):

So the limits of integration are given below:
\[\int\int_R\sin y^3~dA=\int_0^4 \int_\sqrt x^2\sin y^3~dy~dx\]
Not sure if there's a closed form for that integral, but I think a numerical solution exists.