1. Questions

Fourier Sine Series Q

I have the function f(x) = cos(x) on the interval from 0 to pi and I need to comput the Fourier sine series.

I have the integral of cos(x) multiplied by sin(nx), I can't figure out a way to integrate them! The "n" gets in the way, what do I do?

  1. 👍
  2. 👎
  3. 👁
Neutral

  1. first sketch a graph of cos x and sin x, sin 2x, sin 3x, sin 4x
    in the interval from 0 to pi
    You will notice that for n = 1 for example, the plus contribution between 0 and pi/2 cancels the negative contribution between pi/2 and pi
    in fact for cos 1x * sin n x dx, only even values of n will contribute for the integral from 0 to pi.
    The general rule for this definite integral is:
    integral from 0 to pi of
    sin ax cos bx dx
    is:
    2a/(a^2-b^2) if (a-b) is odd
    0 if (a-b) is even
    so here:
    2/(1-n^2) if n is even
    0 if n is odd

    1. 👍
    2. 👎
    Damon

  2. So basically, that is the coefficient "bn" that I place in the summation from n=1 to infinity of sin(nx)?

    If that is correct, thanks, I was going into a complicated page of integration . . .

    1. 👍
    2. 👎
    Anonymous

  4. Okay, I got it, thanks Damon.

    1. 👍
    2. 👎
    Neutral

  5. yes :)

    1. 👍
    2. 👎
    Damon

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    Let f be the function with f(0) = 1/ (pi)^2, f(2) = 1/(pi)^2, and the derivative given by f'(x) = (x+1)cos ((pi)(x)). How many values of x in the open interval (0, 2) satisfy the conclusion of the Mean Value Theorem for the

  2. Calculus

    Let f be a function with second derivative given by f''(x)=sin(2x)-cos(4x). How many points of inflection does the graph of f have on the interval [0,10]? (A)Six (B)Seven (C)Eight (D)Ten (E)Thirteen

  3. Calculus

    The function f is continuous on the open interval (-π, π). If f(x)=cos(x)-1/xsin(x) for x≠0, what is the value of f(0)?

  4. calculus

    g(t)=2+cos t; [0,pi] Can you help me find the average rate of change of the function over the given interval?

  1. Calculus

    A particle moves along the x-axis with position function s(t) = e^cos(x). How many times in the interval [0, 2π] is the velocity equal to 0? 1< My answer 2 3 More than 3 I don't really get this question will someone please

  2. Pre-Cal: Word Problem

    I'm having a lot of trouble on this word problem. Can someone help me plz? To define the inverse sine function, we restrict the domain of sine to the interval ______. On this interval the sine function is one-to-one, and its

  3. Algebra 1

    Question 9 Examine the graph of f(x) f ( x ) and the table that contains values of g(x). g ( x ) . Curve f of x approaches Y equals negative 7 on the left and positive infinity on the right. It passes through points (0, negative

  4. math

    Consider the function f ( x ) = 3x^3 − 3x on the interval [ − 4 , 4 ] . Find the average or mean slope of the function on this interval. By the Mean Value Theorem, we know there exists at least one c in the open interval ( −

  1. Calculus Help!!

    Region R is bounded by the functions f(x) = 2(x-4) + pi, g(x) = cos^-1(x/2 - 3), and the x axis. a. What is the area of the region R? b. Find the volume of the solid generated when region R is rotated about the x axis. c. Find all

  2. calculus

    The first derivative of the function f is given by f'(x) = (cos^2x)/x - 1/5 How many critical values does f have on the open interval (0,10)?

  3. Math - PreCalc (12th Grade)

    The function f(x) = 2x + 1 is defined over the interval [2, 5]. If the interval is divided into n equal parts, what is the value of the function at the right endpoint of the kth rectangle? A) 2+3k/n B) 4+3k/n C) 4+6k/n D) 5+6k/n

  4. Math

    Using the Fundamental Theorem of Calculus solve: F(x)= ∫ Cos(t^2) + t dt on interval [x to 2] FTC = [∫f(x)]' on interval [0 to x] Switching a and b change the sign of the function, since we want to x to be the upper bound,

You can view more similar questions or ask a new question.