how to integrate double integral over rectangle?

Question

amistre64 · Answer

rectangles are simple;  x = a to b, y = c to d

amistre64 · Answer

|dw:1363791471157:dw|

$$\int_{x=a}^{x=b}\int_{y=c}^{y=d} f(x,y)~dydx$$

anonymous · Answer

how to find the limits?

anonymous · Answer

how will you know if you must integrate first with respect to y and with respect to x?

unklerhaukus · Answer

the order dosent change the result,

anonymous · Answer

is it possible that i integrate only with respect to x or with respect to y?

unklerhaukus · Answer

it depends how your rectangle is defined

unklerhaukus · Answer

how is your rectangle defined?

anonymous · Answer

ah..ok tnx..

amistre64 · Answer

assuming by rectangle you mean:|dw:1363868575040:dw|

then the limits are constants and not functions .... the order would be irrelevant.

if you mean by rectangle something that is more skewed in the xy plane:|dw:1363868672091:dw|

it gets more complicated