Evaluate the following integrals by first reversing the order of integration. ∫(0,8)∫(y^(1/3),2) 8e^x^2 dxdy. Why is the limit when you reverse 0

Question

Evaluate the following integrals by first reversing the order of integration. ∫(0,8)∫(y^(1/3),2) 8e^x^2 dxdy. Why is the limit when you reverse 0<=x<=2, 0<=y<=x^3 and not x^3<=y<=8?

anonymous · Answer

I'm confused with finding the limits for each when you reverse the order anyone got any tips?

turingtest · Answer

drawing out the region of integration is almost always a good idea

turingtest · Answer

|dw:1352232985691:dw|

anonymous · Answer

Yeah I got that too, but can't you say y^(1/3) to 8 is the limit? Go along the curve y=x^3 and stop at 8?

turingtest · Answer

well what would the area between y^(1/3) and y=8 look like?

turingtest · Answer

or rather x^3<=y<=8

anonymous · Answer

ohh

anonymous · Answer

it'd be the shaded area under y=8 but above y=x^3?

anonymous · Answer

which we're not looking for right

turingtest · Answer

|dw:1352233420315:dw|you got it :)