Question

What is the definite integral of 0?

Answer 1

There's no single answer if there were to be no boundaries. Since there are boundaries:

`d/(dx)[C] = 0` where `C` is any constant.

`int_a^b f(x)dx` can be taken as `sum_(x_i=a)^(b) f(x_i) Deltax_i`, so with `f(x) = 0`:

`sum_(x_i=a)^(b) 0 Deltax_i = 0sum_(x_i=a)^(b) Deltax_i = 0`

Or, you could say that `f(x) = 0`, thus it has no area between itself and the x-axis when restricted to a boundary.