Conceptual double integral question

1. Nov 4, 2012

Mdhiggenz

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

∫∫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 -y1/3 to y1/3. and the outer integral from 0 to 8. The book however set the inner integral from 0 to y1/3. However we both got the same answer, is there a reason for this?

Thanks

Higgenz

2. Relevant equations

3. The attempt at a solution

2. Nov 4, 2012

tiny-tim

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

3. Nov 4, 2012

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?

4. Nov 4, 2012