(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 T by the first 5 terms.(d) What is the upper bound for your error of your estimate if you use the first 6 terms? (Use thealternating series estimation.) 40Evaluate the integral: /dxx2 + 4(a)Your answer should be in the form kT, where k is an integer. What is the value of k?d1-arctan(x)dxHint:x2 + 1k(b) Now, let's evaluate the same integral using a power series. First, find the power series for thefunction f(x)40. Then, integrate it from 0 to 2, and call the result S. S should be an infinitex2 + 4series.What are the first few terms of S?aoa1a2aza4

2 40 (a) Evaluate the integral: dx x2 + 4 Your answer should be in the form kT, where k is an integer. What is the value of k? d Hint: arctan(x) dx 1 x² + 1 k = (b) Now, let's evaluate the same integral using a power series. First, find the power series for the 40 function f(x) Then, integrate it from 0 to 2, and call the result S. S should be an infinite x² + 4 series.