Solved Example on Trapezoidal Rule
Example 1: Find the area enclosed by the function f(x) between x = 0 to x = 4 with 4 intervals.
f(x) = 4
Solution:
Here a = 0, b = 4 and n = 4.
The trapezoidal rule for n = 4 is,
Substituting the values in this equation,
Example 2: Find the area enclosed by the function f(x) between x = 0 to x = 3 with 3 intervals.
f(x) = x
Solution:
Here a = 0, b = 3 and n = 3.
The trapezoidal rule for n = 3 is,
Substituting the values in this equation,
Example 3: Find the area enclosed by the function f(x) between x = 0 to x = 2 with 2 intervals.
f(x) = 2x
Solution:
Here a = 0, b = 2 and n = 2.
The trapezoidal rule for n = 2 is,
Substituting the values in this equation,
Example 4: Find the area enclosed by the function f(x) between x = 0 to x = 3 with 3 intervals.
f(x) = x2
Solution:
Here a = 0, b = 3 and n = 3.
The trapezoidal rule for n = 3 is,
Substituting the values in this equation,
Example 5: Find the area enclosed by the function f(x) between x = 0 to x = 4 with 4 intervals.
f(x) = x3 + 1
Solution:
Here a = 0, b = 4 and n = 4.
The trapezoidal rule for n = 4 is,
Substituting the values in this equation,
Example 6: Find the area enclosed by the function f(x) between x = 0 to x = 4 with 4 intervals.
f(x) = ex
Solution:
Here a = 0, b = 4 and n = 4.
The trapezoidal rule for n = 4 is,
Substituting the values in this equation,
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.