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It says the answer is 32? How do I go about solving this thing? Thanks

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- Sep 30th 2007, 07:11 AMjst706Riemann sum question
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It says the answer is 32? How do I go about solving this thing? Thanks - Sep 30th 2007, 09:00 AMJhevon
do you recall the definition of a finite Riemann sum?

Let the endpoints be $\displaystyle a = 1$ and $\displaystyle b = 1$, and $\displaystyle n = 2$ be the number of subintervals.

then $\displaystyle \Delta x = \frac {b - a}{n} = \frac {5 - 1}2 = 2$

if each subinterval is of equal length, then each will be 2 units long. the midpoints would be at $\displaystyle x = 2$ and $\displaystyle x = 4$

Thus, $\displaystyle R_2 = \sum_{i = 1}^{2}f(x_i) \Delta x = f(2) \Delta x + f(4) \Delta x$

just plug in the values and work them out