Help with double integral and switching the order of the differentials

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SUMMARY

The discussion focuses on evaluating the double integral of the function e-x2 over a triangular domain defined by the limits 0 to y/2 for x and 0 to 1 for y. Participants emphasize the importance of visualizing the integration region by graphing the function and suggest switching from horizontal to vertical strips for easier computation. The integral can be rewritten as ∫y=01 ∫x=y/21/2 e-x2 dx dy to clarify the limits of integration.

PREREQUISITES
  • Understanding of double integrals in calculus
  • Familiarity with the function e-x2 and its properties
  • Ability to graph functions and interpret integration limits
  • Knowledge of switching the order of integration
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  • Practice evaluating double integrals with triangular regions
  • Learn techniques for switching the order of integration in double integrals
  • Explore graphing tools for visualizing functions and integration limits
  • Study the properties of the Gaussian function e-x2 and its applications
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Students studying calculus, particularly those focusing on double integrals and integration techniques, as well as educators seeking to enhance their teaching methods in this area.

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Homework Statement


1 1/2
∫ ∫ e-x2 dx dy
0 y/2

Homework Equations



***Graph equation***

The Attempt at a Solution


I graphed the function and they made a horizontal strip. However, I can't seem to find the right function with a vertical strip, which is where I'm stuck.
 
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xnitexlitex said:

Homework Statement


1 1/2
∫ ∫ e-x2 dx dy
0 y/2

Homework Equations



***Graph equation***

The Attempt at a Solution


I graphed the function and they made a horizontal strip. However, I can't seem to find the right function with a vertical strip, which is where I'm stuck.

The domain of integration is a triangle. Can you describe it?
 
Last edited:
It might be easier to see if you write the integral
[tex]\int_{y=0}^{y=1}\int_{x= y/2}^{x= 1/2} e^{-x^2}dx dy[/tex]

Draw the graphs corresponding to the limits of integration.
 

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