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(z) dz T2 +1 (b) Now, let's evaluate the same integral using a power series. First, find the power series for the function 16 f(z) = Then, integrate it from 0 to 2, and call the result S. S should be an infinite series. z2 + 4 What are the first few terms of S? 8 32 a2 20 128 az 112 512 576 ag = || ||

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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i need solution for a3

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:
dz
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(z) =
Then, integrate it from 0 to 2, and call the result S. S should be an infinite series.
z2 + 4
What are the first few terms of S?
32
a2 =
20
128
ar =
112
512
ag =
576
||
Transcribed Image Text: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: dz 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(z) = Then, integrate it from 0 to 2, and call the result S. S should be an infinite series. z2 + 4 What are the first few terms of S? 32 a2 = 20 128 ar = 112 512 ag = 576 ||
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