# Homework Help: Limit of double integration

1. Aug 13, 2012

### trap101

For the following regions in R2 express the double integral in terms of iterated integrals in two different ways:

S = the region between the parabolas y = x2 and y = 6 - 4x -x2

Solution:

Ok I got everything except one limit of integraton in regards to the order dx dy of integration:

for an upper limit of integration the solution said: x = -2 ± (10 - y )1/2. my question is how do they obtain that limit of integration. It's probably more of an algebraic question than calculus.

Also how do you write integrals with iTex code?

2. Aug 13, 2012

### BruceW

look at the equations you have been given. Can you think of how to rearrange one of them to get the limit?

Also, for more information on latex: https://www.physicsforums.com/showthread.php?t=617567 Or google might help. I think I remember the way to write the integral sign is \int

3. Aug 13, 2012

### trap101

That's exactly my problem I can't see how to rearrange them to obtain that solution.

4. Aug 14, 2012

### HallsofIvy

Integrating with respect to x should be straightforward. Looking at a graph indicates that, integrating with respect to y you will need to break this into three separate integrals, from y= 0 to y= 1, from y= 1 to y= 9, and from y= 9 to y= 10. Do you see why?

5. Aug 15, 2012

### trap101

I do somewhat see why, well what I mean by that is I understand exactly the reason for splittiing it up, I think the way I drew the graph doesn't illustrate that. But it is solving for the exact x value that I specified in my first post. I tried to work it backwards and couldn't get anything related to what I have.

6. Aug 15, 2012

### BruceW

You can do it. Get y=6-4x-x2 so that x is the subject of the equation. Also, it is important to draw out the graph, and algebraically work out the points of intersection.