Reverse the order of integration

In summary, the conversation discusses the concept of reversing the order of integration and determining the new limits. The example given is for integration of dydx with the limits y=2x, y=2, 0<=x<=1. The method for finding the new limits is to draw a graph of the given equations and determine the region of integration.
  • #1
nothGing
14
0
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?
 
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  • #2
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?

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.
 
  • #3
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?
 
  • #4
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?
 

FAQ: Reverse the order of integration

What does it mean to "reverse the order of integration"?

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.

When should I consider reversing the order of integration?

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.

How do I reverse the order of integration in a double integral?

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.

Can the order of integration be reversed in a triple integral?

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.

Are there any limitations to reversing the order of integration?

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.

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