## allsmiles 3 years ago 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?

1. allsmiles

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

2. TuringTest

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

3. TuringTest

|dw:1352232985691:dw|

4. allsmiles

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?

5. TuringTest

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

6. TuringTest

or rather x^3<=y<=8

7. allsmiles

ohh

8. allsmiles

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

9. allsmiles

which we're not looking for right

10. TuringTest

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

11. TuringTest

so in the area we want we want y bounded above by the function, not the line

12. allsmiles

it's so hard to see sometimes but got it thanks so much for your help!!

13. allsmiles

so whenever you want it bounded by the curve you'd take it from 0 to the curve?

14. TuringTest

welcome, and never underestimate the power of making sure your drawings are correct

15. allsmiles

or where ever it starts at