calculus

suppose

x
S f(t) dt= x^2 - 2x + 1. Find f(x).
1

S = integral and 1 = lower level, x = upper

i don't understand what i'm supposed to find/what to do

  1. 👍
  2. 👎
  3. 👁
  1. did you mean "Find f(t)" ?

    let f(t) = at^2 + bt + c

    then the integral of f(t) by dt from t = 1 to t = x
    = ax^2 + bx + c - (a + b + c)
    = ax^1 + bx - a - b

    comparing this with x^2 - 2x + 1 gives
    a=1
    b=-2 and
    -a -b = 1 This last equation is true,
    and c could be anything

    so f(t) = t^2 - 2t + c

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    Suppose the integral from 2 to 8 of g of x, dx equals 5, and the integral from 6 to 8 of g of x, dx equals negative 3, find the value of the integral from 2 to 6 of 2 times g of x, dx . 8 MY ANSWER 12 16 4

  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. math

    suppose x S f(t) dt= x^2 - 2x + 1. Find f(x). 1 S = integral and 1 = lower level, x = upper i don't understand what i'm supposed to find/what to do and i didn't make any typos.

  4. Physics, Calculus(alot of stuff together)= HELP!!

    A rod extending between x=0 and x= 14.0cm has a uniform cross- sectional area A= 9.00cm^2. It is made from a continuously changing alloy of metals so that along it's length it's density changes steadily from 2.70g/cm^3 to

  1. 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,

  2. Quick calc question

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

  3. calculus

    1.Evaluate the integral. (Use C for the constant of integration.) integral ln(sqrtx)dx 2. Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the curves about the given axis. y =

  4. 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

  1. calc

    Suppose the integral from 2 to 10 of g of x, dx equals 10 and the integral from 8 to 10 of g of x, dx equals negative 6, find the value of the integral from 2 to 8 of one-half times g of x, dx .

  2. calculus integrals

    Evaluate the integral by making the given substitution. (Use C for the constant of integration. Remember to use absolute values where appropriate.) integral x^5/x^6-5 dx, u = x6 − 5 I got the answer 1/6ln(x^6-5)+C but it was

  3. Calculus

    A population of rabbits starts off at time = 0 with 225 rabbits and increases at a rate of r(t) rabbits per month, where t is in months. A. What does the expression (24 integral 36)r(t)dt represent? B. What does the expression 225

  4. Calculus

    Suppose the integral from 2 to 6 of g of x, dx equals 12 and the integral from 5 to 6 of g of x, dx equals negative 3 , find the value of the integral from 2 to 5 of 3 times g of x, dx. A. 45

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