Question

If f(3)=13, f' is continuous, and the integral from 3 to 5 f'(x)dx=24 then the value of f(5) is ?

Answer 1

`f(5) = 37`
See explanation below.

Explanation:

Since `AA x, f'(x) = f'(x)`, `f` is a primitive function of `f'`.

Therefore, `int_3^5 f'(x) dx = f(x) |_3^5 = f(5) - f(3) = f(5) - 13 = 24` by the fundamental theorem of calculus (part 2) (because `f'` is continuous and thus integrable).

Thus, `f(5) = 24 + 13 = 37`.