# Double integral problem

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

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

My answer:

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

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

## Answers and Replies

malawi_glenn
Science Advisor
Homework Helper
looks ok.

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

malawi_glenn
Science Advisor
Homework Helper
seems too easy for 10 marks. There's barely three lines of working there.

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

well I dont 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 :)