Limit of an n-ary product

Question

Since a definite integral is defined as $$\lim_{n\to\infty} \sum_{i=0}^n f(x_i^*)\,\Delta x = \int_a^b f(x)\,dx$$ and the integral is much easier to calcluate than a sum, if we change the sum to a product: $$\lim_{n\to\infty} \prod_{i=0}^n f(x_i^*)\,\Delta x = \text{?}$$ What would be the simpler form of that expression, which, like an integral, would be easier to calculate, if it exists?

Answer 1

It seems that this is a product integral, which can be written as:

$$\prod_a^b{f(x)^{dx}}$$