Double integral absolute value.

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SUMMARY

The discussion focuses on evaluating a double integral involving the absolute value function. The user correctly splits the integral into two parts: one for the range from 0 to 1 and another from -1 to 0. The integrals are expressed as [integral from 0 to 1 [integral from x to -2x (e^(x+y)) dy] dx] and [integral from -1 to 0 [integral from -x to 2x (e^(x+y)) dy] dx]. The key takeaway is to ensure the correct identification of upper and lower boundaries based on the values of x.

PREREQUISITES
  • Understanding of double integrals in calculus
  • Familiarity with the concept of absolute value in mathematical expressions
  • Knowledge of integration techniques for functions of two variables
  • Ability to interpret and manipulate inequalities involving variables
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  • Review the properties of double integrals in calculus
  • Study the application of absolute value in integration
  • Learn about changing the order of integration in double integrals
  • Explore examples of integrals involving exponential functions
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Students studying calculus, particularly those focusing on double integrals and absolute value functions, as well as educators looking for examples to illustrate these concepts.

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Homework Statement



I just need to know if what i did is correct. The question is as follows:

http://imgur.com/1RL7e

1RL7e.png


Homework Equations





The Attempt at a Solution



What I did is as follows:

I split this integral into two parts and solved.


[integral from 0 to 1 [integral from x to -2x (e^(x+y)) dy] dx] +
[integral from -1 to 0 [integral from -x to 2x (e^(x+y)) dy] dx]


The way of thinking about it is that y goes from x to -2x when x goes from 0 to 1 and -x to 2x when x goes from -1 to 0.

Is that right?
 
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Yep, the idea is good, just check which boundary is the upper and which is the lower one.
For example, if 0 < x < 1, then -2|x| = -2x < 0 and |x| = x > 0.
 

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