Question

Integrate the following with respect to x.

If f'(x) = `1/x` and f(1) = `pi/4`, then find f(x)

Answer 1

f'(x) = `1/x`

f(x) = `int "f'"(x)  "d"x = int 1/x  "d"x`

f(x) = log|x| + c

f(1) = `pi/4

⇒ `log|1| + "c" = pi/4`

⇒ 0 + c = `pi/4`

∴ c = ``pi/4`

∴ Required f(x) = `log|x| + pi/4`