How to square a piecewise function? :/

Click For Summary
SUMMARY

The discussion centers on squaring a piecewise function defined as f(x) = 0 for [-π, -π/2), f(x) = π for [-π/2, π/2), and f(x) = 0 for [π/2, π). The correct approach to squaring this function involves calculating f(x)² for each interval, resulting in f(x)² = 0 for [-π, -π/2) and [π/2, π) and f(x)² = π² for [-π/2, π/2). The user initially confused the operation by attempting to sum the function values before squaring, which is incorrect. The key takeaway is to evaluate the function at specific intervals before squaring.

PREREQUISITES
  • Understanding of piecewise functions
  • Basic knowledge of squaring functions
  • Familiarity with mathematical notation and intervals
  • Concept of harmonic functions in physics
NEXT STEPS
  • Study the properties of piecewise functions in calculus
  • Learn about squaring functions and their implications in mathematical analysis
  • Explore harmonic functions and their applications in physics
  • Practice problems involving piecewise function transformations
USEFUL FOR

Students studying calculus, particularly those dealing with piecewise functions and their applications in physics, as well as educators looking for examples of function transformations.

Brown Arrow
Messages
101
Reaction score
0
how to square a piecewise function? urgent :/

Homework Statement


square the following piecewise function
f(x)= 0 [-pi,-pi/2)
pi [-pi/2,pi/2)
0 [pi/2,pi)

Homework Equations


N/A


The Attempt at a Solution


so i think this is how you do it:
(0)2 + (pi)2 +(0)2 is this ocrrect?

or is it the following:

(0+pi+0)2? I am so lost:/

( I am trying to find the energy of the kth harmonic so i need to square the function first) :/

thanks in advance
BA
 
Physics news on Phys.org


Why do you expect that the square of a piecewise function has the same value everywhere?

You just need to calculate f(x)² which can give different values depending on what x is.
 

Similar threads

  • · Replies 14 ·
Replies
14
Views
2K
  • · Replies 9 ·
Replies
9
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 11 ·
Replies
11
Views
3K
Replies
4
Views
2K
Replies
30
Views
3K
  • · Replies 7 ·
Replies
7
Views
3K
  • · Replies 40 ·
2
Replies
40
Views
5K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K