48 (a) Evaluate the integral: 13 + 4 Your answer should be in the form Ki, where & is an integer. What is the value of k? d 1 Hint: di -arctan (@) = I2 + 1 k = (b) Now, let's evaluate the same integral using a power series. First, find the power series for the function f(z) = 48 . Then, integrate it from 0 to 2, and call the result S. S should be an infinite series. 13 + 4 What are the first few terms of S? (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. (d) What is the upper bound for your error of your estimate if you use the first 11 terms? (Use the alternating series estimation.)