(a) Evaluate the integrat: Si 40 dc 2? +4 Your answer should be in the form ko, where k is an integer. What is the value

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A Evaluate The Integrat Si 40 Dc 2 4 Your Answer Should Be In The Form Ko Where K Is An Integer What Is The Value 1 (46.81 KiB) Viewed 20 times

(a) Evaluate the integrat: Si 40 dc 2? +4 Your answer should be in the form ko, where k is an integer. What is the value of k? d Hint: arctan() dz k= 5 1 x2 +1 (b) Now, let's evaluate the same integral using a power series. First, find the power series for the function () 2 +4 Then, integrate it from 0 to 2, and call the result S. S should be an 40 infinite series A What are the first few terms of S? 00 09 ay = 04 (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 win terms of an infinite series. Approximate the value of a by summing the first 5 terms. (d) What is the upper bound for your error of your estimate if you use the first 10 terms? (Use the alternating series estimation)