Evaluate the integral \(\iint_R(x+y)\ dA\) where \(R\) is the region bounded by \(y=1\), \(x=0\), and \(y=x^2\). 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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\(\int_0^1 \int_{x^2}^{1} \left(x+y\right) \, dy\ dx=\int_0^1 \int_{0}^{\sqrt y} \left(x+y\right) \, dx\ dy= \frac{13}{20}\)