Evaluate the integral \(\iint_R(xy)\ dA\) where \(R\) is the region bounded by \(y=0\), \(x=2\), and \(y=x^3\). Check your solution below after you have done the calculation. You may want to set up the integral both ways to see which appears easier.
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\(\int_0^2 \int_{0}^{x^3} \left(xy\right) \, dy\ dx=\int_0^8 \int_{\sqrt[3]{y}}^{2} \left(xy\right) \, dx\ dy= 16\)