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Unformatted text preview: ( x ) and simplify. F ( x) = ∫ t 3 + 1 dt 3 b. Find the average value of f ( x ) = 2 x 2 − 1 over [‐1,2]. 12. a. Use a Riemann sum with 4 equal subintervals and right endpoint evaluation points to approximate the area under the graph of y = x 2 over the interval [0,2]. Is this approximation an overestimate, underestimate, or neither? Explain. b. For the region described in a) find the exact area by taking the limit as n → ∞ of a Riemann sum with n equal subintervals and right endpoint evaluation points. You n
n( n + 1)
may use the following in your computation: ∑ c = cn ∑ i = 2
i =1 n( n + 1)(2 n +...
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