Consider the function f(t)=2sec^2(t)–6t^2 . Let F(t) be the antiderivative of f(t) with F(0)=0 .
Then F(5)=?

I am confused on how I would find the antiderivative, after I do that do I plug in five?

  1. 👍
  2. 👎
  3. 👁
  1. You might want to use a table of integrals for the first term. Most people prefer to call the "antiderivative" the (indefinite) integral.

    In your case the integral is
    F(t) = 2 tan t -2t^3 + C
    where C is an arbitary constant.
    Since F(0) = 0, C = 0
    Now solve for F(5)

    1. 👍
    2. 👎
  2. when i plug this answer in I get -500 is this correct?

    1. 👍
    2. 👎
  3. I get 2 tan 5 - 2*125 = -249.8

    The "5" is understood to be in radians. The -2t^3 term dominates

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus!!!

    Find f. (Use C for the constant of the first antiderivative and D for the constant of the second antiderivative.) f ''(x) = 8 + x3 + x5

  2. Antiderivatives

    For the function f, given below, find the antiderivative F that satisfies F(1)=1. f(x)= x^5 -4x^-3 -4 . I keep getting x^6/6 +x^2 -4x + 17/6 . But my answer is wrong My other answer of x^6/6 +4x^-2 +4x + 43/6 is wrong also. They

  3. Calculus

    The velocity function is v(t)=t^2−5t+4 for a particle moving along a line. Find the displacement and the distance traveled by the particle during the time interval [-1,5]. So I found the antiderivative of the function, which

  4. pre cal 2

    Find all solutions in the interval [0, pi], 2sec^2x+tan^2x-3=0

  1. Calculus

    Consider the function f(x)=(7/x^2)-(6/x^6). Let F(x) be the antiderivative of f(x) with F(1)=0. Then F(2) equals _____.

  2. calculus2

    Evaluate the integral using the indicated trigonometric substitution. (Use C for the constant of integration.) ∫√((x^2-4)/x)dx x=2sec(t)

  3. Calculus Help and Check

    1)Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative. Remember to use ln |u| where appropriate.) f(x) = (1/5)−(3/x) -----> (x/5)-3lnx+C

  4. Calculus

    Which of the following functions of x can be integrated with respect to x without integration by parts, and purely using integration by u-substitution and the knowledge of the antiderivative of the tangent function? a) x^2tan(x^2)

  1. 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

  2. Calculus

    If f is the function defined by f(x)=(x^2+4x)^(1/3) and g is an antiderivative of f such that g(5)=7, then g(1) Is congruent to


    Consider the function f(x)=9x3−4x5. Let F(x) be the antiderivative of f(x) with F(1)=0. Then F(4) =

  4. Calculus 1

    Find the most general antiderivative of the function. Use C for any needed constant. f(u) = (u^4 + 7 sqrt(u)) / u^2 F(u) =

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