Choose a value in which the intervals will be divided, i.e., the value of n. So, for the given expression, first, we will divide the interval into six equal parts as the number of intervals should be even.
Calculate the value of h = (b - a)/2
Evaluate and calculate the values of x0 to xn. Consider y = f(x) and calculate the values of y0 to yn for x0 to xn. Here, we get the following data:
Put the values in the method and then we can calculate approximate value of integral using formula
Stop
In numerical analysis, Simpson's 1/3 rule (method) is a technique for approximating definite integral.
This method is based on Newton's Cote Quadrature Formula and Simpson 1/3 rule is obtained when we put value of n = 2 in this formula.
Read lower limit of integration, upper limit of
integration and number of sub interval
Calculate: step size = (upper limit - lower limit)/number of sub interval
Set: integration value = f(lower limit) + f(upper limit)
Set: i = 1
If i > number of sub interval then goto
Calculate: k = lower limit + i * h
If i mod 2 =0 then
Integration value = Integration Value + 2* f(k)
Otherwise
Integration Value = Integration Value + 4 * f(k)
End If
Increment i by 1 i.e. i = i+1 and go to step 7
Calculate: Integration value = Integration value * step size/3
Display Integration value as required answer
In numerical analysis, Simpson's 1/3 rule (method) is a technique for approximating definite integral. This method is based on Newton's Cote Quadrature Formula and Simpson 1/3 rule is obtained when we put value of n = 2 in this formula.
Read lower limit of integration, upper limit of
integration and number of sub interval
Calculate: step size = (upper limit - lower limit)/number of sub interval
Set: integration value = f(lower limit) + f(upper limit)
Set: i = 1
If i > number of sub interval then goto
Calculate: k = lower limit + i * h
If i mod 3 =0 then
Integration value = Integration Value + 2* f(k)
Otherwise
Integration Value = Integration Value + 3 * f(k)
End If
Increment i by 1 i.e. i = i+1 and go to step 7
Calculate: Integration value = Integration value * step size*3/8
Display Integration value as required answer
In numerical analysis, Simpson's 3/8 rule (method) is a technique for approximating definite integral of a continuous function.
This method is based on Newton's Cote Quadrature Formula and Simpson 3/8 rule is obtained when we put value of n = 3 in this formula.
