Average value of sin(x) integral of sin(x)/x

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SUMMARY

The average value of sin(x) between 0 and π/2 is calculated using the integral of sin(x) from 0 to π/2 divided by π/2. The integral of sin(x)/x does not directly provide the average value of sin(x) over this interval. MATLAB can be used to compute the integral of sin(x) for this purpose, but the correct approach involves understanding the relationship between the integral and the average value formula. The discussion highlights a common misconception regarding the use of sin(x)/x in this context.

PREREQUISITES
  • Understanding of definite integrals
  • Familiarity with the concept of average value of a function
  • Basic knowledge of MATLAB for numerical integration
  • Knowledge of trigonometric functions, specifically sin(x)
NEXT STEPS
  • Learn how to compute definite integrals in MATLAB
  • Study the average value theorem for integrals
  • Explore the properties of the sinc function, sin(x)/x
  • Investigate numerical methods for evaluating integrals
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Mathematics students, educators, and anyone interested in numerical analysis or trigonometric functions will benefit from reading this discussion.

NoobixCube
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This isn't a homework question by the way
I was trying to think what the average value of sin(x) was between 0 and pi/2.
I came to the conclusion it must be integral of sin(x)/x evaluated at those bounds. But I tried to do that in MATLAB to no avail.
Any help would be awesome
 
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How did you come to that conclusion? The average value of sin(x) between pi/2 and 0 is the integral of sin(x) from 0 to pi/2 divided by pi/2. See http://archives.math.utk.edu/visual.calculus/5/average.1/index.html.
 


thanks for your reply. Brain was clearly switched off and now I feel foolish :blushing:
 

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