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?
Limit of an n-ary product
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calculus
integration
limits
notation
products
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3http://math.stackexchange.com/questions/137399/is-there-a-continuous-product?rq=1 is related and I believe will place your question in the right context. – 2012-11-23
1 Answers
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It seems that this is a product integral, which can be written as:
$\prod_a^b{f(x)^{dx}}$