1. The problem statement, all variables and given/known data The problem is attached in this post. 2. Relevant equations The problem is attached in this post. 3. The attempt at a solution I used shell's method and set up my integral as 2π∫(4-x)(x^2)dx, from -2 to 2 and got an answer of 128π/3 which is incorrect. The actual answer is 40π/3. I set my radius as 4-x and I set my height as x^2. To calculate the limits of integration with respect to x (since I used shell's method), I set x^2=2 and got -2 and 2.