(a) Evaluate the integral: Your answer should be in the form ka, where k is an integer. What is the value of k? d 1 Hint: -arctan(r) da 2² +1 k = (b) Now, let's evaluate the same integral using a power series. First, find the power series for the function Then, integrate it from 0 to 2, and call the result S. S should be an infinite series. 16 f(x) = 2² +4 What are the first few terms of S? ao a1 a2 || a4 || 16 x²+4 || a3 = || dx (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 in terms of an infinite series. Approximate the value of by the first 5 terms.

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