Refer to the previous problem for context. Suppose you need to integrate some specific function f. From experimental data, you know that f"(x) = e-² and that X -0.5 -0.25 0 0.25 0.5 f(x) 10 8 9 7 11 (a) Calculate the approximation T4 for the integral 0.5 -0.5 f(x) dx to at least 3 decimal places. (b) Find the maximum that the error might be, E(4), for the above approximation to at least 3 decimal places. (c) Combining the previous two parts, determine an interval which is guaranteed to contain the true value of the integral. Provide at least 3 decimal places for the endpoints.
Refer to the previous problem for context. Suppose you need to integrate some specific function f. From experimental data, you know that f"(x) = e-² and that X -0.5 -0.25 0 0.25 0.5 f(x) 10 8 9 7 11 (a) Calculate the approximation T4 for the integral 0.5 -0.5 f(x) dx to at least 3 decimal places. (b) Find the maximum that the error might be, E(4), for the above approximation to at least 3 decimal places. (c) Combining the previous two parts, determine an interval which is guaranteed to contain the true value of the integral. Provide at least 3 decimal places for the endpoints.
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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