nothGing said: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?
Reversing the order of integration refers to changing the order in which the limits of integration are evaluated when solving a multiple integral. This is often done to simplify the integral or to make it easier to evaluate.
Reversing the order of integration is useful when the original order of integration is difficult to evaluate or when the resulting integral is simpler with the limits in a different order. It is also helpful when the original integral is in terms of a variable that is difficult to integrate with respect to.
To reverse the order of integration in a double integral, simply switch the order of the limits of integration. For example, if the original integral is ∫∫f(x,y)dxdy, the reversed integral would be ∫∫f(x,y)dydx.
Yes, the order of integration can be reversed in a triple integral just like in a double integral. The limits of integration are switched in the same way as in a double integral, but the order in which the variables are integrated may also need to be changed.
Yes, there are limitations to reversing the order of integration. It may not always be possible to reverse the order, especially in more complex integrals. Additionally, the resulting integral may not always be simpler or easier to evaluate after reversing the order of integration.