Calculus

Show that the function F(x) = integral[x to 3x](1/t)dt is constant on the interval (0, +∞).

asked by David
  1. F' = (1/(3x))*3 - (1/x)*1 = 1-1 = 0
    so, F is constant

    posted by Steve

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    How can I show that the function F (x)= the integral from 2x to 5x of 1/ t dt is constant on the interval (0, +∞).
  2. Calculus

    Use the midpoint rule with n=4 to approximate the region bounded by y=-x^3 and y=-x Show that the function f(x)= (integral from 2x to 5x) (1)/(t) dt is constant on the interval (0,+infinity)
  3. unique solution

    How do I show that the equation x^4 + 3x + 1 = 0, -2 <= x <= -1 has exactly one solution in the interval. Thanks. One way to do this is to use trial and error. split the interval (-2,-1) into 10 equal parts. Then evaluate
  4. calculus

    consider the function f(x) = e^x(sinNx) on the interval [0,1] where N is a positive integer. a) Compute the integral from 0 to 1 of f(x). Evaluate this integral when N=5, N=10, and N=100. B) What happens to the graph and to the
  5. calculus

    consider the function f(x) = e^x(sinNx) on the interval [0,1] where N is a positive integer. a) Compute the integral from 0 to 1 of f(x). Evaluate this integral when N=5, N=10, and N=100. B) What happens to the graph and to the
  6. Calculus Help Please Urgent!!!

    Prove that the integral on the interval [a,b] of x is equal (b^2-a^2)/2 integral a to be (x)dx = (b^2-a^2)/2 using the definition of a Definite Integral. This is the limit of a sum approach. show steps please!!! Thank you!!!
  7. Math

    a) Is ∫[-1 to 1]e^x^3 dx positive, negative, or zero? Explain. I think is positive but i don't know how to explain it. b) Explain why 0 < ∫[0 to 1] e^x^2 dx <3. Can you type this equation or whatever in a better
  8. calculus

    LEt f and g be continous functions with the following properties i. g(x) = A-f(x) where A is a constant ii. for the integral of 1 to 2 f(x)dx= the integral of 2 to 3 of g(x)dx iii. for the integral from 2 to 3 f(x)dx = -3A a find
  9. calculus

    LEt f and g be continous functions with the following properties i. g(x) = A-f(x) where A is a constant ii. for the integral of 1 to 2 f(x)dx= the integral of 2 to 3 of g(x)dx iii. for the integral from 2 to 3 f(x)dx = -3A a find
  10. calculus

    In the following problem, suppose f(x) is continuous (and differentiable) function on the interval (0,1). Suppose also that for 0 < x<(1/4) f(x) is negative, for (1/4) <x<1 f(x) is positive, f(1/4)=0, f (2/3)=1, f '

More Similar Questions