How to Apply Trapezoidal Rule?
The trapezoidal rule finds the area under the curve by dividing the area under the curve into various trapezoids and then find the sum of all the trapezoids. The trapezoidal rule is not the perfect approximation of the value of the definite integral as it uses the quadratic approximation.
We have to find the value of the definite integral, ∫ba f(x) dx. The value of the definite integral can be calculated using the trapezoidal rule by following the steps below,
Step 1: Mark the value of sub-intervals, “n” and intervals “a” and “b”.
Step 2: Find the width of sub-interval (△x) using the formula △x = (b – a)/n
Step 3: Put all the values in the trapezoidal rule formula and find the approximate area of the given curve which represents the definite integral ∫ba f(x) dx
∫ba f(x) dx ≈ (Δx/2) (f(x0)+2 f(x1)+2 f(x2)+2 f(x3)+ … +2f(xn-1) + f(xn))
where, xi = a + i△x
Trapezoidal Rule
The trapezoidal rule is one of the fundamental rules of integration which is used to define the basic definition of integration. It is a widely used rule and the Trapezoidal rule is named so because it gives the area under the curve by dividing the curve into small trapezoids instead of rectangles.
Generally, we find the area under the curve by dividing the area into smaller rectangles and then finding the sum of all the rectangles, but in the trapezoidal rule the area under the curve is divided into trapezoids, and then their sum is calculated. The trapezoidal rule is used to find the value of the definite integrals in numerical analysis. This rule is also called the trapezoid rule or the trapezium rule. Let us learn more about the trapezoidal rule, its formula and proof, example, and others in detail in this article.
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