Par COf the attach question pls 216(a) Evaluate the integral:dax² + 4Your answer should be in the form kn, where k is an integer. What is the value of k?d-arctan(x)da1Hint:%3Dx² + 1k =2(b) Now, let's evaluate the same integral using a power series. First, find the power series for the16function f(x) =Then, integrate it from 0 to 2, and call the result S. S should be an infinitex2 + 4°series.What are the first few terms of S?ao =ai =a2 =az =a4 =(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 r in terms of an infinite series.Approximate the value of T 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 thealternating series estimation.)

Name: Par COf the attach question pls 216(a) Evaluate the integral:dax² + 4Y
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: Par COf the attach question pls 216(a) Evaluate the integral:dax² + 4Your answer should be in the form kn, where k is an integer. What is the value of k?d-arctan(x)da1Hint:%3Dx² + 1k =2(b) Now, let's evaluate the same integral using a power series. F

In the given question we already calculated first two parts. Answers from part a) was, ∫0216x2+4dx=2π Answer form part b) was, ∫0216x2+4dx=8-83+3220-128112+512576. . . 0=8-2.67+1.6-1.1429+0.89 . . . 0≈6.6793c) Now, the aproximate value of π by first 5 terms is, 2π=6.6793π=3.33965