Numerical Methods2D

Numerical Integration - Theory & Concepts - Trapezoidal Rule

Numerical methods for evaluating definite integrals.

Approximating the integral of $f(x)$ from $a=0$ to $b=0.8$ using multiple segments.

Number of Segments (n): 2

1 Segment20 Segments

Step Size (h)

0.4000

Exact Value

1.640533

Approximate Integral (Area)

1.068800

Formula

I \approx \frac{h}{2} \left[ f(x_0) + 2 \sum_{i=1}^{n-1} f(x_i) + f(x_n) \right]

True Percent Relative Error:

34.8504%

As n increases, the error approaches zero.

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