Question: Here is a \(2 \mathrm{D}\) region \(\mathbb{R}\) bounded by

\(x=y^{2}\) on the right

\(y=1\) on the top

and \(x=0\) on the left

1. Fill in the boxes with the appropriate values to calculate the double integral \(\iint_{\mathbb{R}} \mathrm{f}[\mathrm{x}, \mathrm{y}] d \mathrm{~A}\).
2. What does \(\iint_{R} 1 d\) A measure?
3. What does \(\iint_{R}\left(x^{3}+y^{2}\right) d A\) measure?

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