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 one year ago
Check my work on changing the order of integration?
\[\int\limits_{0}^{1} \int\limits_{0}^{x^3} e^{x}\sin(y)dydx\]
 one year ago
Check my work on changing the order of integration? \[\int\limits_{0}^{1} \int\limits_{0}^{x^3} e^{x}\sin(y)dydx\]

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xartaan
 one year ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{0}^{1} \int\limits_{0}^{y^{1/3}} e^{x}\sin(y)dxdy\]

xartaan
 one year ago
Best ResponseYou've already chosen the best response.0I just drew a picture, and since I had y=x^3 I figured solving for x gives y^(1/3) .. Am I close, or way off?

xartaan
 one year ago
Best ResponseYou've already chosen the best response.0I guess it didn't copy well in the initial post, here is the original ntegral: \[\int\limits_{0}^{1} \int\limits_{0}^{x^3} e^{x}\sin(y)dydx\]

xartaan
 one year ago
Best ResponseYou've already chosen the best response.0Ok cool, that is what my sketch looked like as well. So I did it right?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\huge \large \int\limits_{y=0}^1\quad\int\limits_{x=y^{1/3}}^1\quad e^x \;\sin y \;dx\;dy\] Hmm like this I think?

xartaan
 one year ago
Best ResponseYou've already chosen the best response.0Isn't x going from 0 to y^1/3 not from 1? I guess I am missing something

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1dw:1362707659927:dwSo this is what our original setup looks like. yes? Y is going from y=0 up to the function.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1We're switching the limits, so now our X will relate to the function.dw:1362707796144:dw

xartaan
 one year ago
Best ResponseYou've already chosen the best response.0oooooooh, I think I see! so x goes from the curve, to the line x=1

xartaan
 one year ago
Best ResponseYou've already chosen the best response.0Ok, last question then. Looking at this, how do I decide wich is at the top of the integral and which is on bottom? My guess is y^1/3 is on top because it is father left than the line x=1, so its smaller values?

xartaan
 one year ago
Best ResponseYou've already chosen the best response.0Wait, smaller value would put it on the bottom.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1We always integrate \(\large \text{left to right}\) and \(\large \text{bottom to top}\). Which in turn will always be smallest to largest, like you said. :)

xartaan
 one year ago
Best ResponseYou've already chosen the best response.0<3 Thank you so much for clearing this up for me!

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1We can see from the picture, that x=y^(1/3) is SMALLER that x=1 in the given interval right? :) Yay glad I could help.
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