# Thread: finding the limits in double integration

1. ## finding the limits in double integration

Sketch the region, R, in the first quadrant bounded by
y=7x, y=4=(x/2), y=(x-2)^2

evaluate, SSr(x+y)dxdy,

what is the limits, and how do i work it out, i have sketch the region already,

2. ## Re: finding the limits in double integration

In this case you have to break the integral up into three integrals - depending on what is the border of the region on the left and right.

top region: x goes from $\displaystyle \frac{y}{7}$ to $\displaystyle +\sqrt{y}+2$
middle region: x goes from $\displaystyle -\sqrt{y}+2$ to $\displaystyle +\sqrt{y}+2$
bottom region: x goes from $\displaystyle -\sqrt{y}+2$ to $\displaystyle 2y$

It might be easier to integrate the other way (dydx instead of dxdy).

- Hollywood

3. ## Re: finding the limits in double integration

Originally Posted by newkidz
Sketch the region, R, in the first quadrant bounded by
y=7x, y=4=(x/2), y=(x-2)^2

evaluate, SSr(x+y)dxdy,

what is the limits, and how do i work it out, i have sketch the region already,
You have a typo, is your second bound y = 4 + (x/2) or y = 4 - (x/2)? Until we know this, we can not say what the bounds of integration are.

4. ## Re: finding the limits in double integration

Originally Posted by Prove It
You have a typo, is your second bound y = 4 + (x/2) or y = 4 - (x/2)? Until we know this, we can not say what the bounds of integration are.
Good point! I read it as y=4 and y=x/2 (and y=7x and y=(x-2)^2, so there are 4 curves in the x-y plane) and I based my answer on that.

- Hollywood