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- anonymous

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?

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- anonymous

- jamiebookeater

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- anonymous

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

- TuringTest

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

- TuringTest

|dw:1352232985691:dw|

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- anonymous

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

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

- TuringTest

or rather x^3<=y<=8

- anonymous

ohh

- anonymous

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

- anonymous

which we're not looking for right

- TuringTest

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

- TuringTest

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

- anonymous

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

- anonymous

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

- TuringTest

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

- anonymous

or where ever it starts at

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