Math Solvers/Algebra & Calculus/numerical-integration

Numerical Integration Solver (Simpson's & Trapezoidal)

Perform numerical quadrature on standard functions (polynomials, trigonometric, exponential, inverse) across user-specified boundaries and subintervals.

Integration Boundaries & Function

Target Integrand f(x)

Lower Limit (a)

Upper Limit (b)

Number of Subintervals (n, even)

Simpson's 1/3 Rule

2.000110

Higher accuracy parabolic quadrature

Trapezoidal Rule

1.983524

Linear piecewise approximation

Step size (h): 0.314159

Evaluated Integral: ∫ f(x) = sin(x) dx from 0 to 3.14159

Quadrature Discretization Steps

1. Integral Limits & Step Interval (h)

Discretized interval [0, 3.14159] into 10 equal subintervals.

2. Trapezoidal Rule Quadrature

Approximates area using linear trapezoids across subintervals.

3. Simpson's 1/3 Rule Quadrature

Higher-order parabolic interpolation yielding superior convergence and accuracy for smooth functions.

Recommended Handbooks & Professional Tools

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Mechanical & ManufacturingIndustry Bible ($120+)

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Mathematical Formulation

Standard analytical and numerical formulations derived from classical algebra, linear algebra, and calculus principles.