# Double integral problem

• Gwilim

#### Gwilim

Evaluate $$\int\ \int_R\ x^2e^ydA$$

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

$$\int\ \int_R\ x^2e^ydA = \int_0^3\ \int_0^1\ x^2e^ydA$$
$$= \int_0^3\ [x^3/3]_0^1 e^y dy$$
$$= 1/3 \int_0^3\ e^ydy$$
$$= 1/3 (e^3-1)$$

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

looks ok.

seems too easy for 10 marks. There's barely three lines of working there.

seems too easy for 10 marks. There's barely three lines of working there.

well I don't know if 10marks is much or not. The integral is easy to solve since you had a rectangular area.

well I don't know if 10marks is much or not. The integral is easy to solve since you had a rectangular area.

The whole 2 hour paper has 100 marks in total. Anyway, thanks for the confirmation.

You are definitely correct. As for the facility with which you did this problem, you're just a superstar at this stuff ;)

Sometimes profs will toss in easy questions to discern who has, at least, a basic command of the principles involved from those who don't even know what an integrand is.

Have confidence! GJ :)