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I have a question that says "Calculate the following Riemann integrals". I know about Riemann sums. Is there any difference between Riemann sums and Riemann integrals?

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The Riemann integral is a limit of Riemann sums. –  Qiaochu Yuan Dec 7 '12 at 23:01
    
so would I just use the same method as I would with a normal Riemann sum question? –  Justin Dec 7 '12 at 23:03
    
thanks by the way –  Justin Dec 7 '12 at 23:05

2 Answers 2

The Riemann integral is that integral defined in terms of limits of Riemann sums (as opposed to, e.g., the Lebesgue integral).

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I suggest you read the definition of the Riemann integral carefully. You will very rarely find a case where a Riemann integral can be calculated by using a sum.

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