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Trapezoidal Rule Calculator
To calculate the area under the curve, enter the function, upper & lower bounds, and the subintervals of the entered function in the trapezoidal rule calculator.
Trapezoidal rule calculator
Trapezoidal rule calculator is used to calculate the approximated integral with the help of the lower & upper bound and the interval of the function.
What is the trapezoidal rule?
The trapezoidal rule is a numerical integration method used to approximate the value of a definite integral by dividing the area under the curve into trapezoids and summing up the areas of those trapezoids.
Formula of Trapezoidal rule:
The formula for the trapezoidal rule is as follows:
a∫b f(x) dx ≈ [Δx / 2] [f(x0) + 2{f(x1) + f(x2) + ... + f(xn-1)) + f(xn)}]
In the above formula:
- Δx = (b – a) / n
- n is the number of trapezoids, used to approximate the area under the curve.
How to calculate the problems of trapezoidal rule?
Example 1:
Calculate the area under the curve 0∫1 e-x^2 dx; if n = 4.
Solution:
Step 1: Calculate “Δx”
Using the trapezoidal rule with n = 4, we have:
Δx = (b – a) / n
Δx = (1 – 0) / 4
Δx = 0.25
Step 2: Calculate the values of the function
f (0) = e0
f (0) = 1
f (0.25) = e (-0.25)2
f (0.25) ≈ 0.968
f (0.5) = e (-0.5)2
f (0.5) ≈ 0.882
f (0.75) = e (-0.75)2
f (0.75) ≈ 0.705
f (1) = e (-1)2
f (1) ≈ 0.368
Step 3: Put the values in the trapezoidal rule formula.
Using the trapezoidal rule formula, we have:
0∫1 e-x2 dx ≈ [(1 – 0) / (2*4)] [1 + 2(0.968) + 2(0.882) + 2(0.705) + 0.368]
0∫1 e-x2 dx ≈ 0.7468
Therefore, the approximate value of the integral using the trapezoidal rule with n = 4 is 0.7468.