# TrapezoidIntegral (3) - Linux Manuals

## TrapezoidIntegral: Integral of a one-dimensional function.

## NAME

QuantLib::TrapezoidIntegral - Integral of a one-dimensional function.

## SYNOPSIS

#include <ql/math/integrals/trapezoidintegral.hpp>

Inherits QuantLib::Integrator.

### Public Member Functions

**TrapezoidIntegral** (Real accuracy, Size maxIterations)

### Protected Member Functions

Real **integrate** (const boost::function< Real(Real)> &f, Real a, Real b) const

## Detailed Description

### template<class IntegrationPolicy> class QuantLib::TrapezoidIntegral< IntegrationPolicy >

Integral of a one-dimensional function.Given a target accuracy $ \psilon $, the integral of a function $ f $ between $ a $ and $ b $ is calculated by means of the trapezoid formula [ int_{a}^{b} f mathrm{d}x = ac{1}{2} f(x_{0}) + f(x_{1}) + f(x_{2}) + ots + f(x_{N-1}) + ac{1}{2} f(x_{N}) ] where $ x_0 = a $, $ x_N = b $, and $ x_i = a+i Delta x $ with $ Delta x = (b-a)/N $. The number $ N $ of intervals is repeatedly increased until the target accuracy is reached.

**Tests**

- the correctness of the result is tested by checking it against known good values.

## Author

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