Evaluate the integral 16 -dx. x² + 4 Your answer should be in the form kr, where k is an integer. What is the value of k? d arctan(x) Hint: 1 dx x² + 1 k = (b) Now, lets evaluate the same integral using power series. First, find the power series for the function 16 f(x) Then, integrate it from 0 to 2, and call it S. S should be an infinite series. x2 + 4 What are the first few terms of S ? ao = aj = a2 = 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 in terms of an infinite series. Apprevimate the value of by the firct 5 tormc

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