Math Problem Statement
Using simpson's rule to approximate sin(x) dx between 0 and pi, how large do we need to choose n so that our approximation is accurate to within 0.001? Also, approximate this interval using simpson's rule with the number of subintervals determined.
Solution
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Math Problem Analysis
Mathematical Concepts
Numerical Integration
Simpson's Rule
Error Analysis
Formulas
Simpson's Rule: ∫_a^b f(x) dx ≈ (h/3) [f(x_0) + 4f(x_1) + 2f(x_2) + ... + f(x_n)]
Error Bound for Simpson's Rule: |E_S| ≤ (M(b - a)^5) / (180n^4)
Theorems
Error Bound for Simpson's Rule
Suitable Grade Level
Grades 11-12 or Undergraduate
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