What is the Trapezoidal Rule?
The trapezoidal rule is a rule which is used to find the value of the definite integral of the form b∫a f(x) dx. We know that the value of the definite integral b∫a f(x) dx is the area enclosed under the curve y = f(x) and the x-axis in the interval a and b on the x-axis. We calculate this area by dividing the complete area into several small rectangles and then finding their sum.
In the Trapezoidal rule as the name suggest the area under the curve is divided into several trapezoids and then their sum is found to get the area of the curve. The trapezoidal rule does not provide the best approximation of the area under the curve than the Simpson’s Rule but still, its result is precise enough and this rule is a widely used rule in calculus.
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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