College Calculus

posted by .

Calculate the average over the given interval. f(x)=sin(pi/x)/x^2, [1,2]

  • College Calculus -

    Let u = 1/x
    du = -dx/x^2

    Int(sin(pi/x)/x^2 dx)[1,2]
    = Int(-sin(pi*u) du)[1,.5]
    = 1/pi cos(pi*u) [1,.5]
    = 1/pi(cos pi/2 - cos pi)
    = 1/pi(0+1)
    = 1/pi

    Since the interval length is 1, the average is just 1/pi

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    Let f be the function given by f(t) = 2ðt + sin(2ðt) a) Find the value of t in the open interval (0,20 for which the line tangent at (t, f(t)) is parallel to the line through (0,0) and (2,4ð) b) Suppose the given function describes …
  2. Calculus II

    With Taylor/Maclaurin polynomials Use the Remainder Estimation Theorem to find an interval containing x = 0 over which f(x) can be approximated by p(x) to three decimal-place accuracy throughout the interval. f(x) = sin x p(x) = x …
  3. calculus

    Calculate he average over the given interval: f(x)=e^(-n*x), [-1,1]. I know that the average value = (1/b-a)integrate from a to b f(x)dx
  4. physics

    In this problem you will determine the average velocity of a moving object from the graph of its position as a function of time . A traveling object might move at different speeds and in different directions during an interval of time, …
  5. calculus

    let f(t) = 2*pi*t + sin(2*pi*t) a) find value of t in open interval (0,2) for which the tangent line at (t, f(t)) is parallel to the line through (0,0( and (2, 4pi) b) suppose the given funtion describes the position of a particle …
  6. Brief Calculus

    Calculate the average rate of change of the given function over the given interval. Where appropriate, specify the units of measurement. f(x) = 1/x;[2, 7] I used the f(b)-f(a)/b-a and I got -.071 and it said I was wrong could you please …
  7. Calculus

    I'm supposed to find the average value of the function over the given interval. f(x) = sin(nx), interval from 0 to pi/n, where n is a positive integer. I know the average value formula, and I know that the integral of that function …
  8. calculus

    Consider the given function and the given interval. f(x) = 4 sin x − 2 sin 2x, [0, π] (a) Find the average value fave of f on the given interval. fave = (b) Find c such that fave = f(c). (Round your answers to three decimal …
  9. calculus multiple choice

    1.The region in the first quadrant bounded by the x-axis, the line x = ln(π), and the curve y = sin(e^x) is rotated about the x-axis. What is the volume of the generated solid?
  10. calculus

    Consider the given function and the given interval. f(x) = 10 sin(x) − 5 sin(2x), [0, π] (a) Find the average value fave of f on the given interval. (b) Find c such that fave = f(c). (Round your answers to three decimal places.)

More Similar Questions