2 16 (a) Evaluate the integral: dæ x² + 4 Your answer should be in the form kT, where k is an integer. What is the value of k? d 1 -arctan(x) dæ Hint: x? + 1 k (b) Now, let's evaluate the same integral using a power series. First, find the power series for the function 16 -. Then, integrate it from 0 to 2, and call the result S. S should be an infinite series. x2 + 4 f(x) = What are the first few terms of S? ao = ai = a2 az = a4 = I| || ||

Question
2
16
(a) Evaluate the integral:
dæ
x² + 4
Your answer should be in the form kT, where k is an integer. What is the value of k?
d
1
-arctan(x)
dæ
Hint:
x? + 1
k
(b) Now, let's evaluate the same integral using a power series. First, find the power series for the function
16
-. Then, integrate it from 0 to 2, and call the result S. S should be an infinite series.
x2 + 4
f(x) =
What are the first few terms of S?
ao =
ai =
a2
az =
a4 =
I| || ||
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Transcribed Image Text

2 16 (a) Evaluate the integral: dæ x² + 4 Your answer should be in the form kT, where k is an integer. What is the value of k? d 1 -arctan(x) dæ Hint: x? + 1 k (b) Now, let's evaluate the same integral using a power series. First, find the power series for the function 16 -. Then, integrate it from 0 to 2, and call the result S. S should be an infinite series. x2 + 4 f(x) = What are the first few terms of S? ao = ai = a2 az = a4 = I| || ||

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