(a) Evaluate the integral: : 1² 24 2² +4 Your answer should be in the form kr, where k is an integer. What is the value of k? k= 3 What are the first terms of S? ao= 12 a1 = (b) Now, let's evaluate the same integral using a power seces. First, find the power series for the function Then, integrate it from 0 to 2, and call the result S. S should be an infinite series. 24 f(x)= = 2²+4 a2= 8 a3 04 IL -4 12 5 1052 315 i 12 T 12. 9 dz > 0 b B (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 in terms of an infinite series. Approximate the value of by the first 5 terms.
(a) Evaluate the integral: : 1² 24 2² +4 Your answer should be in the form kr, where k is an integer. What is the value of k? k= 3 What are the first terms of S? ao= 12 a1 = (b) Now, let's evaluate the same integral using a power seces. First, find the power series for the function Then, integrate it from 0 to 2, and call the result S. S should be an infinite series. 24 f(x)= = 2²+4 a2= 8 a3 04 IL -4 12 5 1052 315 i 12 T 12. 9 dz > 0 b B (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 in terms of an infinite series. Approximate the value of by the first 5 terms.
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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Question
Please give me answer very fast in 5 min mon
Transcribed Image Text:24
z² +4
Your answer should be in the form kn, where k is an integer. What is the value of k?
k= 3
(a) Evaluate the integral: Sº²
(b) Now, let's evaluate the same integral using a power series. First, find the power series for the function
Then, integrate it from 0 to 2, and call the result S. S should be an infinite series.
24
f(x)
2²+4
What are the first terms of S?
do 12
a1 =
-4
12
a2= 5
a3 =
a4=
in
1052
315
12
12
9
A
da
>
b b
>
>
X
9
>
B
(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 in terms of an infinite series.
Approximate the value of x by the first 5 terms.
>
B
(d) What is the upper bound for the error of an estimate of if you use the first 10 terms? (Use the
alternating series estimation.)
3.0418
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