In this problem you will calculate by using by using the formal definition of th

Question

In this problem you will calculate by using by using the formal definition of the definite integral: The interval [0,4] is divided into n equal subintervals of length delta x. What is delta x (in terms of n)? Delta x = The right-hand endpoint of the kth subinterval is denoted x*k. What is x*k (in terms of k and n)? x*k = Using choices for x*k. and delta x, the definition tells us that What is f(x*k) delta x (in terms of k and n)? f(x*k) delta x = Express in closed form. (Your answer will be in terms of n.) Finally, complete the problem by taking the limit as n rightarrow infinity of the expression that you found in the previous part.

Explanation / Answer

Delta x = 4/n x*_k = 4k/n f(x*_k)*Delta x = [64(k^2)/(n^3)] + (12/n) Sigma f(x*_k)*Delta x = (100/3) + (32/n) + (32/(2n^2)) lim = 100/3

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