Fourier Series (differentiation)

Click For Summary

Homework Help Overview

The discussion revolves around the integration of the function sin(t)cos(nt) with specific conditions applied to the variable t. The context involves Fourier series and differentiation, particularly focusing on integration techniques.

Discussion Character

  • Exploratory, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • Participants are exploring integration techniques, particularly substitution, and questioning the appropriate variable to set for u. There is also a suggestion to evaluate specific cases to identify patterns.

Discussion Status

The discussion is ongoing, with participants seeking hints and clarification on the integration process. Some guidance has been offered regarding evaluating specific cases and considering trigonometric identities.

Contextual Notes

There are indications of uncertainty regarding the integration limits and the specific approach to take, with some participants expressing confusion about the setup of the problem.

driedupfish
Messages
27
Reaction score
0

Homework Statement



sin(t)cos(nt) dt

Homework Equations


The Attempt at a Solution


I tried setting u=sin(t) or cos(nt) or nt but none seems to work. Can someone give me a hint as what to set u equal to? Thanks.
 
Physics news on Phys.org
Are you trying to integrate? Over what range?
 
Pengwuino said:
Are you trying to integrate? Over what range?
The function is as follow:
f(t)= 0, -pi ≤ t ≤ 0
sint, 0 ≤ t ≤ pi

≤ (less than or equal to)

I just don't know what to set u equal to, I am thinking of using integration by substitution.
 
Can someone give me some hints please?
 
I would start by trying the first few cases by hand n=0, n=1, n=2, n=3, etc.. and see if a pattern develops, both on result and how to evaluate

look at some trig formulas for angle sums & double angle may help before looking at substitution
 

Similar threads

Fourier series of this scale and shift of triangle wave
  • · Replies 1 ·
Replies
1
Views
2K
How should I show that solutions can be expressed as a Fourier series?
  • · Replies 3 ·
Replies
3
Views
2K
Complex Fourier Series Problem
  • · Replies 5 ·
Replies
5
Views
2K
A few questions to make sure I understand Fourier series
  • · Replies 3 ·
Replies
3
Views
2K
Show uniqueness in Dirichlet problem in unit disk
  • · Replies 6 ·
Replies
6
Views
2K
Find the Fourier Series of the function
  • · Replies 12 ·
Replies
12
Views
2K
Compute sum (possibly using Parseval's formula)
  • · Replies 1 ·
Replies
1
Views
2K
Solve integral by finding Fourier series of complex function
  • · Replies 3 ·
Replies
3
Views
2K
On pointwise convergence of Fourier series
  • · Replies 3 ·
Replies
3
Views
2K
Fourier series for trigonometric absolute value function
  • · Replies 8 ·
Replies
8
Views
3K