Question

What is `f(x) = int 1/x` if `f(2)=1`?

Answer 1

`ln(x/2)+1`

Explanation:

The derivative of `lnx=1/x`

hence the anti-derivative of `1/x" is"lnx`

`rArrF(x)= int1/x dx=lnx+c`

To find c , use f(2) = 1

ln2 + c = 1 → c = 1 - ln2

`rArr F(x)=lnx+1-ln2`

using `• lnx-lny=ln(x/y)"to simplify"`

`rArr int1/x dx= ln(x/2)+1`