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chjopl
- 21
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For F(x) dx from a to b show TRAP(n)=Left(n) + 1/2 (f(b)-f(a))*delta x
Trapezoid integration, also known as the trapezoidal rule, is a numerical method used for approximating the definite integral of a function. It involves dividing the interval of integration into smaller trapezoids and calculating the area under each trapezoid to estimate the total area under the curve.
Trapezoid integration works by using the formula: ∫f(x) dx ≈ (b-a) * [(f(a) + f(b))/2], where a and b are the limits of integration and f(x) is the function being integrated. This formula calculates the area of a trapezoid by taking the average of the function's values at the two endpoints of the interval and multiplying it by the width of the interval.
Trapezoid integration is a simple and easy-to-use method for approximating integrals. It also provides a more accurate estimate compared to other basic numerical methods, such as the midpoint rule. Additionally, it can be used to approximate the integral of non-smooth functions that may not be easily integrated analytically.
One limitation of trapezoid integration is that it can only provide an approximation of the integral, not the exact value. Also, the accuracy of the approximation depends on the number of trapezoids used, so a large number of trapezoids may be needed for complex functions. Additionally, trapezoid integration may not work well for functions with sharp peaks or discontinuities.
Trapezoid integration is commonly used in fields such as physics, engineering, and economics to approximate the area under curves and solve problems that involve integrals. It is also used in computer programming for numerical integration and in statistics for approximating probabilities.