Math Problem Statement
Suppose you are going to estimate
I=∫40cos3xdx.
using the trapezoidal rule.
According to the error bound, what is the minimum number of points nmin needed to guarantee that the absolute value of the error is less than 10−7 ?
Solution
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Math Problem Analysis
Mathematical Concepts
Numerical Integration
Trapezoidal Rule
Error Bound
Formulas
Trapezoidal Rule Error Bound: E_T ≤ (b - a)^3 / 12n^2 * max|f''(x)|
Second derivative of cos(3x): f''(x) = -9cos(3x)
Theorems
Error Bound Theorem for Numerical Integration
Suitable Grade Level
University Level - Numerical Analysis
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