How to Reverse order of integration.
Double integral of (x+2y)
Region is : y=1+x^2 to y=2x^2, x=0, x=1, dy dx
edit : Question explicitly states reverse order of integration. I graphed out the region of integration... tried out the obvious x=(y-1)^(1/2) to x=(y/2)^(1/2) and y=0 to y=2, dxdy, but i got a complex number from square root of -1 ... from (0-1)^(1/2) ...
so i tried out various other combinations such as x=0 to x=(y/2)^(1/2) and y=0 to y=1+x^2 ... and worked them out one by one to see if the answer matches the original using an online calculator (save time)... all don't return the same answer. think main problem i have is choosing 4 boundaries when the region graphed has only three surfaces.

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- schrodinger

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- anonymous

to reverse the order of integration, you just switch the limits on the integral to match dx or dy

- anonymous

|dw:1338673816726:dw|

- anonymous

edited question with more details on the problem im having

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- anonymous

sorry can't read the drawing its a bit messy

- anonymous

i can redo the drawing but the general idea for reversing the integration is to reverse the limits and reverse dx and dy... i think you're making it a bit too complicated

- anonymous

|dw:1338674746475:dw|

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