EXAMPLE 21.5 Multiple-Application Version of Simpson’s 1/3 Rule Problem Statement: Use Eq. with = 4 to estimate the integral of (21.18) n From = 0 to = 0.8. Recall that the exact integral is 1.640533. a b Solution: From Eq. (21.19), The estimated error is: The previous example illustrates that the application version of Simpson’s 1/3 rule yields very accurate results. For this reason, it is considered superior to the trapezoidal rule for most applications. However, it is limited to cases where the values are equispaced. Further, it is limited to situations where there are an even number of segments and an odd number of points. Consequently, an formula known as Simpson’s 8/3 rule is used in conjunctions
EXAMPLE 21.5 Multiple-Application Version of Simpson’s 1/3 Rule Problem Statement: Use Eq. with n = 4 to estimate the integral of (21.18) From a = 0 to b = 0.8. Recall that the exact integral is 1.640533. Solution: From Eq. (21.19), The estimated error is: The previous example illustrates that the application version of Simpson’s 1/3 rule yields very accurate results. For this reason, it is considered superior to the trapezoidal rule for most applications. However, it is limited to cases where the values are equispaced. Further, it is limited to situations where there are an even number of segments and an odd number of points. Consequently, an formula known as Simpson’s 8/3 rule is used in conjunctions