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.

are you bex?

check out this post and my reply

http://www.jiskha.com/display.cgi?id=1196473338

To find f(x), we need to evaluate the integral on the left-hand side of the equation. Let's break down the problem step by step:

1. First, let's rewrite the integral equation we have:

∫[1 to x] f(t) dt = x^2 - 2x + 1

2. Next, we'll differentiate both sides of the equation with respect to x. This is known as the Fundamental Theorem of Calculus. Since we have a definite integral, we'll need to use the Chain Rule:

d/dx [∫[1 to x] f(t) dt] = d/dx [x^2 - 2x + 1]

3. By applying the Chain Rule on the left-hand side, we get:

f(x) = d/dx [x^2 - 2x + 1]

4. Now, let's differentiate the right-hand side:

f(x) = 2x - 2

5. Therefore, the function f(x) that satisfies the given integral equation is:

f(x) = 2x - 2

To summarize, to find f(x), we differentiated both sides of the integral equation with respect to x, and determined that f(x) = 2x - 2.

To solve this problem, we need to find the function f(x) when the integral of f(t) dt from 1 to x is equal to x^2 - 2x + 1.

Let's break down the problem step by step:

Step 1: Write the integral equation.
∫(from 1 to x) f(t) dt = x^2 - 2x + 1

Step 2: Take the derivative of both sides.
d/dx [∫(from 1 to x) f(t) dt] = d/dx (x^2 - 2x + 1)

Step 3: Apply the Fundamental Theorem of Calculus.
f(x) = d/dx (x^2 - 2x + 1)

Step 4: Differentiate the right side of the equation.
f(x) = 2x - 2

Therefore, the function f(x) is given by f(x) = 2x - 2.