# Thread: Evaluating a repeated integral

1. ## Evaluating a repeated integral

The question is:

$\int_{0}^{1}\int_{0}^{x}(5-3x-2y)dydx$

First I have to evaluate the repeated integral, which (I think) I can manage. But it then says "Then sketch the region of integration, reverse the order of integration, and evaluate the reverse integral."

Now again, once I've understood the first bit of that question, I could probably evaluate the integral, but I don't know how to sketch the region of integration, or how to reverse the order of integration. Can anyone help?

2. Originally Posted by chella182
The question is:

$\int_{0}^{1}\int_{0}^{x}(5-3x-2y)dydx$

First I have to evaluate the repeated integral, which (I think) I can manage. But it then says "Then sketch the region of integration, reverse the order of integration, and evaluate the reverse integral."

Now again, once I've understood the first bit of that question, I could probably evaluate the integral, but I don't know how to sketch the region of integration, or how to reverse the order of integration. Can anyone help?
Hi

Have a look to the sketch above

To compute $\int_{0}^{1}\int_{0}^{x}(5-3x-2y)dydx$
the area involved is the right-down triangle
For a given x value (between 0 and 1), y can go from 0 to x (red line)

To reverse the integral you can see that for a given y value (between 0 and 1), x can go from y to 1 (green line)

Therefore integral is $\int_{0}^{1}\int_{y}^{1}(5-3x-2y)dxdy$

3. Thankyou I'm still not 100% with it, but my friend on my course has managed to tackle the question successfully, so hopefully he can shed some more light on the matter.
The annoying thing is I was in the lecture for reversing the order as well! I don't know how I'm so rubbish at it.