Double Integrals: Sketch Region, Reverse Order & Evaluate

[math_04]

Homework Statement

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.

Homework Equations

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.

 

[rocomath]

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

 

[mathfied]

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

 

[Hurkyl]

Or, just have a modicum of patience. Sheesh!

 

[math_04]

there it is lol. finally got approved

 

[Hurkyl]

there it is lol. finally got approved

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

 

[math_04]

any answer to my question lol?

 

[HallsofIvy]

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

 

[math_04]

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

 

[Defennder]

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