(a) Evaluate the integral 40 S. dr. x²+4 Your answer should be in the form ka, where k' is an integer. What is the value

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A Evaluate The Integral 40 S Dr X 4 Your Answer Should Be In The Form Ka Where K Is An Integer What Is The Value 1 (46.38 KiB) Viewed 20 times

(a) Evaluate the integral 40 S. dr. x²+4 Your answer should be in the form ka, where k' is an integer. What is the value of k? darctan(z) (Hint: dz k = 5 40 (b) Now, lets evaluate the same integral using power series. First, find the power series for the function f(x) = Then, integrate it from 0 to 2, and call it S. S should be an infinite series an- n=0 What are the first few terms of S? ao 20 aj -20/3 a2= 4 a3 = -20/7 a4 = 20/9 (c) The answer in part (a) equals the sum of the infinite series in part (b) (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. 1052/315 (d) What is an upper bound for your error of your estimate if you use the first 12 terms? (Use the alternating series estimation.)