# Double Integrals

1. Jul 12, 2008

### math_04

1. The problem statement, all variables and given/known data

Consider the integral shown in the attached diagram. Sketch the region of integration, express the integral with the reverse order of integration and evaluate it leaving your answer in surd form.

2. Relevant equations

3. The attempt at a solution

I have drawn the region in the diagram and hope its correct.

I am getting the limits for the reversed order as 0<=x<=1 and for y i am not sure. I tried but i ended up with the same thing square root of x <= y <= 1. That is definitely not right! Could anyone please help me out?

The way I do it is for x limits for the reversed order, I draw a horizontal line passing through the sketched region and for the y limits, it is a vertical line passing through the sketched region. Is there a more effective way cause i keep getting stuck with this method?

Thanks heaps.

Thanks.

#### Attached Files:

• ###### Double Integral-1.JPG
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2. Jul 12, 2008

### rocomath

Link your picture elsewhere b/c who knows how long it will take for your attachment to be approved.

3. Jul 12, 2008

### mathfied

upload the picture in imageshack.us mate
it gives a direct link to the picture. good site for hosting pics.

4. Jul 12, 2008

### Hurkyl

Staff Emeritus
Or, just have a modicum of patience. Sheesh!

5. Jul 12, 2008

### math_04

there it is lol. finally got approved

6. Jul 12, 2008

### Hurkyl

Staff Emeritus
Yes, that 72 minute wait was soooo oppressive. :tongue:

7. Jul 13, 2008

### math_04

any answer to my question lol?

8. Jul 13, 2008

### HallsofIvy

Staff Emeritus
The region with y from $\sqrt{x}$ to 1 is above the parabola. In youur picture you have shaded the area below the parabola.

9. Jul 13, 2008

### math_04

ohhh yeaaa haha cheers for that. but are the limits right?

10. Jul 13, 2008

### Defennder

He just answered your question. The limits for y is incorrect because they describe the region above the y=x^(1/2) curve.