- #1

- 114

- 1

## Homework Statement

Suppose I have d/dx f(x) = 0, and I integrate both sides with respect to x. I have worked out two possibilities, and I am not sure which is correct:

1) ∫ d/dx f(x) dx = 0 → ∫ f'(x) dx = 0 → f(x) + C = 0

or

2) ∫ d/dx f(x) dx = 0 → d/dx ∫ f(x) dx = 0 → d/dx (F(x) + C) = 0 → f(x) = 0

where F(x) is the integral of f(x) and f'(x) is the derivative of f(x), both with respect to x.

Thanks.