Math Problem Statement

Solution

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Math Problem Analysis

Mathematical Concepts

Numerical Integration
Trapezoidal Rule
Midpoint Rule
Simpson's Rule
Definite Integral

Formulas

Trapezoidal Rule: T_n = (h/2) * [f(x0) + 2Σ f(xi) + f(xn)]
Midpoint Rule: M_n = h * Σ f((xi-1 + xi)/2)
Simpson's Rule: S_n = (h/3) * [f(x0) + 4Σ f(x_odd) + 2Σ f(x_even) + f(xn)]

Theorems

Numerical Approximation Theorems
Composite Rules for Numerical Integration

Suitable Grade Level

Undergraduate Calculus