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xartaan
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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
 one year ago
xartaan Group Title
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
 one year ago

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

xartaan Group TitleBest ResponseYou've already chosen the best response.0
I 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?
 one year ago

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

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
dw:1362707277183:dw
 one year ago

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

zepdrix Group TitleBest 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?
 one year ago

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

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

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

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

xartaan Group TitleBest ResponseYou've already chosen the best response.0
Ok, 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?
 one year ago

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

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
We 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. :)
 one year ago

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

zepdrix Group TitleBest ResponseYou've already chosen the best response.1
We 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.
 one year ago
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