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anonymous
 one year ago
Can someone walk me through how to switch the order of integration on some double integrals?
anonymous
 one year ago
Can someone walk me through how to switch the order of integration on some double integrals?

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\text{Original integral:}~\int_0^1\int_{y/2}^{1/2}e^{x^2}dxdy\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I tried changing the bounds, and I got \[\int_0^{1/2}\int_0^{2x}f(x,y)dydx\]Am I on the right track so far?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Im kind of confused on what to do next though.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3start with the inner integral : \[\large \int_0^{1/2} \color{blue}{\int_0^{2x}e^{x^2}dy}~dx\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0OH! I forgot that I can actually integrate it now. So, it becomes: \[\int_0^{1/2}2xe^{x^2}dx=(e^{x^2})_0^{1/2}=1e^{1/4}\]Is that right?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3Perfect! you may use wolfram to double check http://www.wolframalpha.com/input/?i=%5Cint_0%5E1%5Cint_%7By%2F2%7D%5E%7B1%2F2%7De%5E%7Bx%5E2%7Ddxdy

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Alright, thanks! I thought I had to do something to the integrand, and I didn't recognize that with the change to dydx, I could actually integrate.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3Thats it! changing order of integration gave us that factor 2x which was useful in usubstitution
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