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Numerical Integration
High School
Definition
Numerical integration approximates definite integral values. Methods include trapezoidal rule and Simpson's rule.
Formulas
∈tₐ^b f(x)dx ≈ (h)/(2)(f(a) + f(b))
Trapezoidal rule (single interval)
∈tₐ^b f(x)dx ≈ (h)/(3)(f(a) + 4f(m) + f(b))
Simpson's 1/3 rule
Examples
Example 1
Calculate ∫₀² x² dx using Simpson's rule.
Applications
Physics
Trajectory calculation
Statistics
Cumulative distribution
Engineering
Area, volume calculation
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