Question

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Answer 1

Step 1: draw the region (triangle)

The diagram shows how you can integrate with respect to y first, then x. (type II)
But then it means that there are two region, and hence the integral must be split in two, one each for D1 and D2.

Answer 2

@rouzam are you with me so far?

Answer 3

The horizontal axis is the x-axis, and the vertical is the y-axis. This is true for all 2-D Cartesian planes. Yes, I should have labelled them.

Answer 4

In general the x and y axes pass through the origin (0,0).

Answer 5

Next step:
Choose the order of integration.
The above diagram shows one way, i.e. dy dx. (it should read type I, I had a typo)
The other option is dx dy, and it looks like this (type II)

This way, there is only one region to worry about, and hopefully less chance of mistakes.
This is the usual choice for most people.

Answer 6

Are you with me?@rouzam

Answer 7

I think he means you plotted (5,0) instead of (0,5)

Answer 8

Now having chosen the type II integration order, we have to work out the limits of integration.
This is the most important part.
Since we integrate first with respect to x, then the limits (two sloping lines) must be expressed in terms of y.
I just realize that I got the triangle backwards. I'll correct it. But the choice of integration order will be reversed, we will choose to integrate dy dx (type I region). The corrected diagram will explain it.

Answer 9

@freckles, yes, thank you.

Answer 10

Now we know the limits, and within the single region D.