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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.

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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(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 the alternating series estimation.)
Transcribed Image Text:(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 the alternating series estimation.)
40 Evaluate the integral: / dx x2 + 4 (a) Your answer should be in the form kT, where k is an integer. What is the value of k? d 1 -arctan(x) dx Hint: x2 + 1 k (b) Now, let's evaluate the same integral using a power series. First, find the power series for the function f(x) 40 . Then, integrate it from 0 to 2, and call the result S. S should be an infinite x2 + 4 series. What are the first few terms of S? ao a1 a2 az a4
Transcribed Image Text:40 Evaluate the integral: / dx x2 + 4 (a) Your answer should be in the form kT, where k is an integer. What is the value of k? d 1 -arctan(x) dx Hint: x2 + 1 k (b) Now, let's evaluate the same integral using a power series. First, find the power series for the function f(x) 40 . Then, integrate it from 0 to 2, and call the result S. S should be an infinite x2 + 4 series. What are the first few terms of S? ao a1 a2 az a4
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