Answer
392.7k+ views
Hint:
Simpson’s rule formula is used to calculate the integral value of any function. It calculates the value of the area under the curve over a given interval by dividing the area into equal parts. It follows the method similar to integration by parts.
Complete step by step solution:
Step – 1 : In order to integrate any function $f(x)$ in the interval $\left( {a,b} \right)$ follow the steps given below.
Select a value for n, which is the number of parts the interval is divided into. Let the value of n be an even number.
Step – 2 : Calculate the width, is denoted by$h$ using formula for find width $\left( h \right) = \dfrac{{b - g}}{n}$
Where a and b denoted the interval $\left( {a,b} \right)$
Step – 3 : Calculate the value of \[{x_0}\] to \[{x_n}\] as \[{x_0} = 9\], \[{x_1} = {x_0} + h,.......{x_{n - 1}} = {x_{n - 2}} + h,{x_n} = b\]
Step – 4 : Substitute all the above found value, in the Simpson’s rule formula to calculate the integral value.
\[\int\limits_a^b {f(x)dx = \dfrac{h}{3}} \left[ {\left( {{y_0} + {y_1}} \right) + y\left( {{y_1} + {y_3} + ... + {y_{n - 1}}} \right) + 2\left( {{y_2} + {y_4} + ... + {y_{n - 2}}} \right)} \right]\]
Note: Integration is the process of measuring the area under a function plotted on a graph. Sometimes, the evaluation of expression involving these integrals can become daunting, if not indeterminate.
Here, we will discuss the Simpson’s $\dfrac{1}{3}$ rule of approximating integrals of the form
\[I = \int\limits_a^b {f(x)dx} \] Where, \[f(x)\] is called integral
a = lower limit of integration
b = upper limit of integration
Simpson’s $\dfrac{1}{3}$ rule is an extension of Trapezoidal rule where the integral is approximated by a second order polynomial.
Note:
Simpson’s rule formula is used to calculate the integral value of any function. It calculates the value of the area under the curve over a given interval by dividing the area into equal parts. It follows the method similar to integration by parts.
Complete step by step solution:
Step – 1 : In order to integrate any function $f(x)$ in the interval $\left( {a,b} \right)$ follow the steps given below.
Select a value for n, which is the number of parts the interval is divided into. Let the value of n be an even number.
Step – 2 : Calculate the width, is denoted by$h$ using formula for find width $\left( h \right) = \dfrac{{b - g}}{n}$
Where a and b denoted the interval $\left( {a,b} \right)$
Step – 3 : Calculate the value of \[{x_0}\] to \[{x_n}\] as \[{x_0} = 9\], \[{x_1} = {x_0} + h,.......{x_{n - 1}} = {x_{n - 2}} + h,{x_n} = b\]
Step – 4 : Substitute all the above found value, in the Simpson’s rule formula to calculate the integral value.
\[\int\limits_a^b {f(x)dx = \dfrac{h}{3}} \left[ {\left( {{y_0} + {y_1}} \right) + y\left( {{y_1} + {y_3} + ... + {y_{n - 1}}} \right) + 2\left( {{y_2} + {y_4} + ... + {y_{n - 2}}} \right)} \right]\]
Note: Integration is the process of measuring the area under a function plotted on a graph. Sometimes, the evaluation of expression involving these integrals can become daunting, if not indeterminate.
Here, we will discuss the Simpson’s $\dfrac{1}{3}$ rule of approximating integrals of the form
\[I = \int\limits_a^b {f(x)dx} \] Where, \[f(x)\] is called integral
a = lower limit of integration
b = upper limit of integration
Simpson’s $\dfrac{1}{3}$ rule is an extension of Trapezoidal rule where the integral is approximated by a second order polynomial.
Note:
Recently Updated Pages
The deliquescent among the following is ACaCl2 BFeSO47H2O class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
The d electron configurations of Cr2 + Mn2 + Fe2 + class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
The degree of ionization of a 01M bromoacetic acid class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
The degree of Hydrolysis of CH3COONH4 is independent class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
The degree of hydrolysis for a salt of strong acid class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
The degree of hydrolysis for a salt of strong acid class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What is the full form of AD a After death b Anno domini class 6 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name 10 Living and Non living things class 9 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)