Method and examples
Numerical integration using Trapezoidal rule
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pi as input implemented on 22.06.2023; like 0 to pi, h = pi/12
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Numerical integration using Trapezoidal rule calculator
1. From the following table, find the area bounded by the curve and x axis from x=7.47 to x=7.52 using trapezodial, simplson's 1/3, simplson's 3/8 rule.
x7.477.487.497.507.517.52
f(x)1.931.951.982.012.032.06

2. Evaluate I = int_0^1 (1)/(x+1) dx by using simpson's rule with h=0.25 and h=0.5


Example
1. Find Solution using Trapezoidal rule
xf(x)
1.44.0552
1.64.9530
1.86.0436
2.07.3891
2.29.0250


Solution:
The value of table for x and y

x1.41.61.822.2
y4.05524.9536.04367.38919.025

Using Trapezoidal Rule
int y dx = h/2 [y_0+y_4 + 2(y_1 + y_2 + y_3)]

int y dx = 0.2/2 [4.0552 + 9.025 + 2xx(4.953 + 6.0436 + 7.3891)]

int y dx = 0.2/2 [4.0552 + 9.025 + 2xx(18.3857)]

int y dx = 4.9852

Solution by Trapezoidal Rule is 4.9852




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