16 dz 12 + 4 (a) Evaluate the integral: Your answer should be in the form kr, where k is an integer. What is the value of k? 1 Hint: arctan(r) dz 22 +1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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16
dz
2 + 4
(a) Evaluate the integral:
Your answer should be in the form kr, where k is an integer. What is the value of k?
Hint:
arctan(z)
|
r2 +1
(b) Now, let's evaluate the same integral using a power series. First, find the power series for the function
16
f(=)
Then, integrate it from 0 to 2, and call the result S. S should be an infinite series.
r2 + 4
What are the first few terms of S?
a, =
32
a2 =
20
128
az =
112
512
a4 =
576
of
of
of
Transcribed Image Text:16 dz 2 + 4 (a) Evaluate the integral: Your answer should be in the form kr, where k is an integer. What is the value of k? Hint: arctan(z) | r2 +1 (b) Now, let's evaluate the same integral using a power series. First, find the power series for the function 16 f(=) Then, integrate it from 0 to 2, and call the result S. S should be an infinite series. r2 + 4 What are the first few terms of S? a, = 32 a2 = 20 128 az = 112 512 a4 = 576 of of of
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