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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?

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math.stackexchange.com/questions/137399/… is related and I believe will place your question in the right context. –  Ittay Weiss Nov 23 '12 at 7:37
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up vote 1 down vote accepted

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

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

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