for the function F(t)=ln(t^2), let f(t)=F'(t). Write the integral from a to b of f(t) dt and evaluate it with the fundamental theorem of calculus.

the integral from 1 to 3 ___ dt= __

  1. 👍
  2. 👎
  3. 👁
  1. F(t) = ln t^2
    = 2 lnt

    f(t) = 2/t

    so if you want ∫f(t) dt from 1 to 3
    = ln t^2 from 1 to 3
    = ln9 - ln1
    = ln9 - 0
    = ln 9

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus (math)

    The volume of the solid obtained by rotating the region enclosed by y=1/x4,y=0,x=1,x=6 about the line x=−2 can be computed using the method of cylindrical shells via an integral. it would be great if you can just even give me

  2. Calc Help Please Again Last one!

    Write out the form of the partial fraction decomposition of the function appearing in the integral: integral (6x-58)/(x^2+2x-63) Determine the numerical values of the coefficients, A and B, where A

  3. Calculus

    Suppose f(x) is a continuous function. Then a function F(x) such that F'(x) = f(x) is called: A.) the indefinite integral of f B.) the antiderivative of f C.) an antiderivative of f D.) a definite integral of f E.) All of the

  4. Calculus check

    The functions f and g are given by f(x)=sqrt(x^3) and g(x)=16-2x. Let R be the region bounded by the x-axis and the graphs of f and g. A. Find the area of R. B. The region R from x=0 to x=4 is rotated about the line x=4. Write,

  1. Calculus

    I am trying to find the integral of e^(6x)sin(7x). Apparently, the answer is (6e^(6x)sin(7x) - 7e^(6x)cos(7x))/85) + C and achieving the answer is mostly understandable since it involves integrating the function in parts... that

  2. Algebra 2

    write a polynomial function of least degree with integral coefficients whose zeros include 4 and 2i

  3. calc: arc length

    find the exact length of this curve: y = ( x^3/6 ) + ( 1/2x ) 1/2

  4. math, calculus

    if f(1)=12 and f' is continuous, what is the value of f(4)? integral from 1 to 4 of f'(x)dx = 17 IF the integral of f'(x) dx from 1 to 4 is 17, as you say, then the function f(x), which is the integral with an arbitrary constant,

  1. calculus (please with steps and explanations)

    consider the function f that is continuous on the interval [-5,5] and for which the definite integral 0(bottom of integral sign) to 5(top of integral sign) of f(x)dx=4. Use the properties of the definite integral to evaluate each

  2. Calculus

    If f(x) and g(x) are continuous on [a, b], which one of the following statements is true? ~the integral from a to b of the difference of f of x and g of x, dx equals the integral from a to b of f of x, dx minus the integral from a

  3. calculus

    8). Part 1 of 2: In the solid the base is a circle x^2+y^2=16 and the cross-section perpendicular to the y-axis is a square. Set up a definite integral expressing the volume of the solid. Answer choices: integral from -4 to 4 of

  4. mathematics

    Use the graph of f(t) = 2t − 5 on the interval [−2, 10] to write the function F(x), where f of x equals the integral from 1 to x of f of t dt. Answer choices: F(x) = 2x − 5 F(x) = x2 − 5x − 4 F(x) = x2 − 5x + 4 F(x) =

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