Conceptual double integral question

[Mdhiggenz]

Homework Statement

∫∫x²sin(y²)dA; R is the region that is bounded by y=x³
y=-x³, and y=8.

While working out the regions for this integral I set the inner integral to -y^1/3 to y^1/3. and the outer integral from 0 to 8. The book however set the inner integral from 0 to y^1/3. However we both got the same answer, is there a reason for this?

Thanks

Higgenz

Homework Equations

The Attempt at a Solution

 

[tiny-tim]

Hi Mdhiggenz!

While working out the regions for this integral I set the inner integral to -y^1/3 to y^1/3. and the outer integral from 0 to 8. The book however set the inner integral from 0 to y^1/3. However we both got the same answer, is there a reason for this?

Either one of you made a mistake, or the book multiplied by 2 after integrating.

 

[Mdhiggenz]

Hey Tim,

Yea the books answer is quite strange, the way I reasoned my answer is when I drew the graph R2: goes from -y^1/3 to positive y^1/3. Unless the book chose not to include the negative region.

Thoughts?

 

[tiny-tim]

Your method looks fine.