Question

Find the volume of the region above the triangle with vertices (0, 2), (1, 1), and (2, 2), and under
the surface z = xy.

If I want to integrate with y first, what should be the limit?

Answer 1

should I be splitting the triangle into two parts and int with y?

Answer 2

I meant MUST I.

Answer 3

1) Come to terms with your equations:

y = 2
y = -x + 2
y = x

2) Decide which way to go.

Either

y = 2 to y = -x+2 for x between 0 and 1 and then y = 2 to y = x for x between 1 and 2

Or

x = y to x = -y + 2 for y between 1 and 2

Let's see if you follow that far.

Answer 4

I see. I've get to the ans. thanks!