Trapezoidal Rule
Q1: What is Trapezoidal Rule?
Answer:
The trapezoidal rule is the rule that is used to find the definite integral it divides the area under the curve into several trapezoids and then their individual area is found and then the sum is calculated to get the value of the definite integral.
Q2: What is the Trapezoidal Rule Formula?
Answer:
The trapezoidal rule formula is,
∫ba f(x) dx = (Δx/2) (f(x0)+2 f(x1)+2 f(x2)+2 f(x3)+ … +2f(xn-1) + f(xn))
Q3: Why is it Called Trapezoidal Rule Formula?
Answer:
Trapezoidal Rule Formula is called the trapezoidal rule because it divides the area under the curve into several trapezoids and then their area is calculated by finding the sum of the trapezoids.
Q4: What is the Difference Between Trapezoidal Rule and Riemann Sums Rule?
Answer:
The major difference between the Trapezoidal rule and Riemann Sums rule is, as the trapezoidal rule divides the area under the curve as the trapezoids and then finds the area by taking their sum whereas, the Riemann Sums divides the area under the curve as the trapezium and then finds the area by taking their sum.
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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