Is the following definition of integrals correct?

Question

I'd imagine the idea of integrals summing up infinite slices would be formalized something like this:

$$\int_{k = 0}^x f \left( k \right) = \lim_{\omega \to \infty} \sum_{k = 0}^\omega f \left( {k x \over \omega} \right)$$

Is this correct?

Answer 1

No it not correct way to write an integration as this infinite sum rather you can write it like this

∫ˣf(k)dk = lim ω---->∞ (1/ω) Σ(k=0,xω)f(k)

I don't know how to type equations, sorry for that.

EDIT: $$\int_0^x f(k)dk=\lim_{\omega\to\infty}\frac{1}{\omega}\sum_{k=0}^{x\omega}f(k)$$