Solving a Double Integral over a Rectangle with Given Vertices

[Gwilim]

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

 

[malawi_glenn]

looks ok.

 

[Gwilim]

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

 

[malawi_glenn]

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.

 

[Gwilim]

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.

 

[BrendanH]

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.

 

[rocomath]

Have confidence! GJ :)