Find the integral of f(x)=32/(x^2+4) in the interval (0,2). Your answer should be in the form kπ, where k is an integer. What is the value of k? k=
a) Find the integral of f(x)=32/(x^2+4) in the interval (0,2).
Your answer should be in the form kπ, where k is an integer. What is the value of k?
k=
(b) Now, lets evaluate the same integral using power series. First, find the power series for the function f(x)=32/(x^2+4). Then, integrate it from 0 to 2, and call it S. S should be an infinite series.
What are the first few terms of S ?
a0=
a1=
a2=
a3=
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 π in terms of an infinite series. Approximate the value of π by the first 5 terms.
(d) What is the upper bound for your error of your estimate if you use the first 7 terms? (Use the alternating series estimation.)
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