Iterated Integral Help!

[mathiscoolz]

I need help on the following iterated integral:



What I attempted to do was draw out the region, then split the absolute value into x=y and x=-y, and that would leave me with two integrals as seen below:



However, I don't get the correct answer. Could someone help me light the way? Thanks!

 

[pka]

I need help on the following iterated integral:

View attachment 3667

Why don't you begin this way: \(\displaystyle \displaystyle\int_{ - 1}^1 {\frac{1}{3}\left[ {{{\left( {1+y} \right)}^3} - {{\left( {\left| y \right|+y} \right)}^3}} \right]dy}~?\)

Now split the integral.