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How many subintervals are required to ensure an approximation error of less than x 10-5 when approximating the integral of cos on [0, 1] and employing 3.3.1 the composite trapezoidal rule? 3.3.2 the composite Simpson's rule?

How many subintervals are required to ensure an approximation error of less than x 10-5 when approximating the integral of cos on [0, 1] and employing 3.3.1 the composite trapezoidal rule? 3.3.2 the composite Simpson's rule?

Advanced Engineering Mathematics
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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3.3 How many subintervals are required to ensure an approximation error of less than x 10-5 when approximating the integral of cosa on [0, 1] and employing 3.3.1 the composite trapezoidal rule? 3.3.2 the composite Simpson's rule?
Transcribed Image Text:3.3 How many subintervals are required to ensure an approximation error of less than x 10-5 when approximating the integral of cosa on [0, 1] and employing 3.3.1 the composite trapezoidal rule? 3.3.2 the composite Simpson's rule?
Expert Solution
Step 1

While approximating the integral: ∫abf(x)dx, the error bound for:

  • Composite trapezoidal rule is M12b-a3n2. Here, f''(x)≤M for a≤x≤b.
  • Composite Simpson's rule is L180b-a5n4. Here, f4(x)≤L for a≤x≤b.
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