.2 16 (a) Evaluate the integral: dr x² + 4 Your answer should be in the form ka, where k is an integer. What is the value of k? d Hint: arctan(x) 1 1² + 1 k = (b) Now, let's evaluate the same integral using a power series. First, find the power series for the 16 function f(x) = . Then, integrate it from 0 to 2, and call the result S. S should be an infinite x² + 4" series. What are the first few terms of S? ao a1 az = a4 = (c) The answers to part (a) and (b) are equal (why?). Hence, if you divide your infinite series from (b) by k (the answer to (a)), you have found an estimate for the value of T in terms of an infinite series. Approximate the value of a by the first 5 terms. (d) What is the upper bound for your error of your estimate if you use the first 7 terms? (Use the alternating series estimation.) || ||

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