Integrating an absolute function

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SUMMARY

The discussion focuses on integrating the function |10^(1/2)*(x^5)+(5*x^(1/5))| from -1 to 1. Participants concluded that to eliminate the absolute value, one must recognize that the function is odd and positive for x > 0, allowing the use of symmetry in integration. The integral can be simplified by calculating twice the integral from 0 to 1, leveraging the properties of even functions.

PREREQUISITES
  • Understanding of definite integrals
  • Familiarity with odd and even functions
  • Knowledge of integration techniques, including product rule
  • Basic algebraic manipulation of functions
NEXT STEPS
  • Study the properties of odd and even functions in calculus
  • Learn integration techniques for composite functions
  • Explore the concept of symmetry in definite integrals
  • Review the product rule in the context of integration
USEFUL FOR

Students studying calculus, particularly those tackling integration problems involving absolute values and symmetry in functions.

steve snash
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Homework Statement



1
⌠ | 10^(1/2)*(x^5)+(5*x^(1/5)) | dx

−1

Homework Equations


once the absolute value is gone you can just integrate the function

The Attempt at a Solution


how do you get rid of the absolute, and how do you then integrate it, do you use the product rule with 10^(1/2)*(x^5)
 
Physics news on Phys.org
Notice the function inside the absolute value signs is an odd function and is positive if x>0. So its absolute value will be an even function. So double the integral from 0 to 1.
 

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