Reverse the order of integration

[nothGing]

why sometime we need to reverse the order of integration?
and how to determine the new limit?
for example: for integration of dydx, the limit of y and x:
y=2x , y=2;
0<=x<=1.
after we reverse the order become dxdy, how to determine the new limit of x and y?

 

[LCKurtz]

why sometime we need to reverse the order of integration?
and how to determine the new limit?
for example: for integration of dydx, the limit of y and x:
y=2x , y=2;
0<=x<=1.
after we reverse the order become dxdy, how to determine the new limit of x and y?

You use the picture to get the limits going in the x direction first, just like you would use the picture going in the y direction first for the dydx integral.

 

[nothGing]

erm..draw de picture..
how about if i don't know how to draw it?
can teach me any method to find the new limit?

 

[LCKurtz]

Draw the graph of y = 2x and y = 2 for x between 0 and 1. It should form a triangle with the y axis. That's the region in question. You know how to do that, right?