- #1

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Over the rectangle R with vertices (0,0), (1,0), (1,3) and (0,3).

**My answer**:

[tex] \int\ \int_R\ x^2e^ydA = \int_0^3\ \int_0^1\ x^2e^ydA [/tex]

[tex] = \int_0^3\ [x^3/3]_0^1 e^y dy[/tex]

[tex] = 1/3 \int_0^3\ e^ydy [/tex]

[tex] = 1/3 (e^3-1) [/tex]

*Double integrals are new to me, so if someome could check my answer that would be greatly helpful*