Reverse the order of integration

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SUMMARY

Reversing the order of integration is essential in double integrals to simplify calculations or adapt to specific problem requirements. In the given example, the original limits for the integral of dydx are defined by the equations y=2x and y=2, with x ranging from 0 to 1. To reverse the order to dxdy, one must analyze the region defined by these limits, which forms a triangle. The new limits for x and y can be determined by visualizing the area and adjusting the bounds accordingly.

PREREQUISITES
  • Understanding of double integrals in calculus
  • Familiarity with the concept of changing the order of integration
  • Ability to sketch graphs of equations
  • Knowledge of determining limits of integration from graphical representations
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  • Learn how to sketch regions defined by inequalities for integration limits
  • Study techniques for changing the order of integration in double integrals
  • Explore examples of reversing integration limits in polar coordinates
  • Practice problems involving double integrals with varying limits
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Students and educators in calculus, mathematicians working with double integrals, and anyone seeking to enhance their understanding of integration techniques.

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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