1. ## [SOLVED] Find f(x)

Find y= f(x) with intergrals?

if $f "(x)= 2x-1$, f ' (1) = 3 and f(0)= 1

Okay for this one, for the first integral I got $x^2 -x+c$. I tested out the F'(1) = 3 and got 0+C=3

Then for the 2nd integral I got $1/3 x^3 - 1/2 x^2 +c$. I tested out f(0) = 1 and got 0-0+c=1

Correct?

Find y= f(x) with intergrals?

if $f "(x)= 2x-1$, f ' (1) = 3 and f(0)= 1

Okay for this one, for the first integral I got $x^2 -x+c$. I tested out the F'(1) = 3 and got 0+C=3

Then for the 2nd integral I got $1/3 x^3 - 1/2 x^2 +c$. I tested out f(0) = 1 and got 0-0+c=1

Correct?

You needed to include $c_1$ before you integrated the second time.

IE $\frac{1}{3}x^3-\frac{1}{2}x^2+\overbrace{3}^{c_1}x+c_2$