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(a) Evaluate the integral: S = 16 x² + 4 dx Your answer should be in the form k, where k is an integer. What is the value of k? d 1 Hint: arctan(r) da x² +1 k=

(a) Evaluate the integral: S = 16 x² + 4 dx Your answer should be in the form k, where k is an integer. What is the value of k? d 1 Hint: arctan(r) da x² +1 k=

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.2: Exponential Functions
Problem 72E
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(a) Evaluate the integral: Hint: arctan(2) k= Your answer should be in the form ki, where k is an integer. What is the value of k? d 1 dx x² +1 a1 az (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. 16 f(x)= x² + 4 What are the first few terms of S? ao = a4 || a3 = S = = = 16 x² + 4 dx (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. (d) What is the upper bound for your error of your estimate if you use the first 7 terms? (Use the alternating series estimation.)
Transcribed Image Text:(a) Evaluate the integral: Hint: arctan(2) k= Your answer should be in the form ki, where k is an integer. What is the value of k? d 1 dx x² +1 a1 az (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. 16 f(x)= x² + 4 What are the first few terms of S? ao = a4 || a3 = S = = = 16 x² + 4 dx (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. (d) What is the upper bound for your error of your estimate if you use the first 7 terms? (Use the alternating series estimation.)
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