Interchange the order of integration and evaluate the integral [0,8]∫ [∛y,2]∫ (e^x^4)dxdy

Answer 1

Draw a diagram. The region is below the curve y = x^3. So,
∫[0,8] ∫[[∛y,2] f(x,y) dx dy = ∫[0,2] ∫[0,x^3] f(x,y) dy dx

Answer 2

how did you get the x^3

Answer 3

x = ∛y, right? y = x^3
This is similar to another problem posted recently -- same region of integration.