In Example 6.22 part b, if you use the first 5 terms of the Maclaurin series (instead of the first 4 terms as in the example), what would the sum be? Answer with 4 decimal places. Note: All 4 decimal places might not be a correct approximation of the integral. Answer with 4 decimal places anyway.EXAMPLE 6.22 Using Taylor Series to Evaluate a Definite Integral _ 2 . . . . a. Express / e x dx as an Infinite series. 1 b. Evaluate J 9Jrz dx to within an error of 0.01. 0 [Sholeide Solution] Solution a. The Maclaurin series for if"2 is given by 2 _ (x ) _ n! n: =1x2+'3:+-- +(1)\"%+ 2n Therefore, b. Using the result from part a. we have 1 a? _ -1 i_i L-... If \"Ix1 3+10 42+216 ' The sum of the first four terms is approximately 0.74. By the alternating series test, this estimate is accurate to within an error of less than 216 2 0.0046296