What is f(x) = int 1/(x+3) dx if f(2) = 0 ?

1 Answer
Dec 7, 2016

The function is f(x) = ln|x + 3| - ln5

Explanation:

We can rewrite this as f(x) = int(x + 3)^-1dx.

Let u = x + 3. Then du = 1(dx) -> dx= du.

f(x) = int(u^-1)dx

f(x) = ln|u| + C

f(x) = ln|x+ 3| + C

We can now solve for C. When x = 2, y= 0.

0 = ln|2 + 3| + C

C = -ln5

:. Therefore, the function is f(x) = ln|x + 3| - ln5.

Hopefully this helps!