Calculus

posted by .

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= __

  • Calculus -

    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

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calc

    d/dx integral from o to x of function cos(2*pi*x) du is first i do the integral and i find the derivative right. by the fundamental theorem of calculus, if there is an integral from o to x, don't i just plug the x in the function. …
  2. vector calculus

    Show that the given line integral is independent of path.Then, evaluate the line integral I by finding a potential function f and applying the Fundamental Theorem of Line Integrals. I=ç_{(0,0)}^{(1,2)}(x+y)dx+(x-y)dy
  3. calculus

    Use the fundamental theorem of calculus to evaluate the following integral ∫^π/2 **the bottom is zeroe. |cosx| dx
  4. Calculus I

    Section The fundamental Theorem of Calculus: Use Part I of the fundamental Theorem to compute each integral exactly. 4 | 4 / 1 + x^2 dx 0
  5. Calculus

    "Leave the answer as a definite integral, but indicate how it could by evaluated by using the fundamental theorem of calculus." I solved the problem to a definite integral. Proceeding via the fundamental theorem, would involve finding …
  6. Calculus Fundamental Theorem

    Evaluate the definite integral. function: x+13 with respect to variable x lower limit:0 upper limit:22
  7. calculus

    a) Let f(z) = z^2 and γ(t) = 1 + it^3, t ∈ [0,1]. i) Write out the contour integral ∫γ f(z)dz as an integral with respect to t. You do not need to evaluate this integral. ii) Evaluate the integral ∫0,1+i …
  8. Calculus

    Use the Fundamental Theorem to evaluate the integral from 0 to 3 of the quantity x cubed minus 6 times x, dx. (Your answer must include the antiderivative.) Use a graph of the function to explain the geometric meaning of the value …
  9. Calculus

    Hi it's me again I need help with this too and I promise to never use this site again! I feel so ashamed for asking :( Use the Fundamental Theorem to evaluate the integral from 0 to 3 of the quantity x cubed minus 6 times x, dx.The …
  10. Calculus

    use te fundamental theorem of calculus to evaluate the integral Integral [0, pi/3] sin^2(x)dx I'm confused on what F(x) should be

More Similar Questions