Reverse the order of integration

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Discussion Overview

The discussion revolves around the need to reverse the order of integration in double integrals, specifically focusing on how to determine the new limits of integration after such a reversal. The context includes mathematical reasoning and potential challenges faced by participants in visualizing the integration region.

Discussion Character

  • Mathematical reasoning
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • Some participants inquire about the necessity of reversing the order of integration and the method for determining new limits.
  • One participant suggests using a graphical representation to identify limits when reversing the order of integration.
  • Another participant expresses uncertainty about how to draw the required graph and seeks alternative methods for finding new limits.
  • A later reply emphasizes the importance of drawing the graph of the given functions to understand the integration region better.

Areas of Agreement / Disagreement

Participants generally agree on the importance of visualizing the integration region, but there is no consensus on methods for those who struggle with drawing the graph.

Contextual Notes

The discussion highlights limitations related to the participants' ability to visualize the integration region, which may affect their understanding of how to determine new limits after reversing the order of integration.

nothGing
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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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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.
 
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?
 
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?
 

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