Calc III Double Integral Question

[dropoutofschool]

View attachment 96628

This is the problem I'm trying to solve. The directions require me to rewrite as a single integral and evaluate. But I'm having trouble setting the bounds for a complete compounded integral. The graph of the region would look something like this...
View attachment 96629

Where the shaded area is the region. I would think its a Type 2 region (dxdy). The y bounds would be 0 to√2 and the x bounds would be from x=sqrt(1-x^2) to x=sqrt(4-x^2)... so so I thought. I then realized that these bounds would extra space outside of the intended shaded region, so the y=x linemust be involved in the bounds somehow.

I just need help setting the integral up, the actual integrating should be easy. Thanks ! Any help is appreciated!

 

[dropoutofschool]

Ugh Pictures didn't post... please refer to this...

 

[Mark44]

View attachment 96628
This is the problem I'm trying to solve. The directions require me to rewrite as a single integral and evaluate. But I'm having trouble setting the bounds for a complete compounded integral. The graph of the region would look something like this...
View attachment 96629
Where the shaded area is the region. I would think its a Type 2 region (dxdy). The y bounds would be 0 to√2 and the x bounds would be from x=sqrt(1-x^2) to x=sqrt(4-x^2)... so so I thought. I then realized that these bounds would extra space outside of the intended shaded region, so the y=x linemust be involved in the bounds somehow.

I just need help setting the integral up, the actual integrating should be easy. Thanks ! Any help is appreciated!

I'm pretty sure the idea is to write the integral in polar form, not in Cartesian form... There's no way you can write this integral in Cartesian form with only one integral.

 

[Mark44]

In the future, please post questions like this in the Homework & Coursework sections (under Calculus), not here in the technical math sections.

 

[dropoutofschool]

WOW! Completely forgot about polar, just completed the problem----for future reference, the answer is 15/16. Thank you sir and will change where I post next time!