Math, asked by saikiranchary108, 3 months ago

in Simpsons rule have 5 ordinates than (n) equals to ?

Answers

Answered by Anonymous
1

Step-by-step explanation:

The Simpson's Rule formula with n=4 segments is written in the form. S4=Δx3[f(x0)+4f(x1)+2f(x2)+4f(x3)+(x4)]. The width of the subinterval is. Δx=b−an=π−04=π4

Answered by js3232745
1

Answer:

Simpson’s Rule is a numerical method that approximates the value of a definite integral by using quadratic functions.

This method is named after the English mathematician Thomas Simpson

(

1710

1761

)

.

Simpson’s Rule is based on the fact that given three points, we can find the equation of a quadratic through those points.

To obtain an approximation of the definite integral

b

a

f

(

x

)

d

x

using Simpson’s Rule, we partition the interval

[

a

,

b

]

into an even number

n

of subintervals, each of width

Δ

x

=

b

a

n

.

On each pair of consecutive subintervals

[

x

i

1

,

x

i

]

,

[

x

i

,

x

i

+

1

]

,

we consider a quadratic function

y

=

a

x

2

+

b

x

+

c

such that it passes through the points

(

x

i

1

,

f

(

x

i

1

)

)

,

(

x

i

,

f

(

x

i

)

)

,

(

x

i

+

1

,

f

(

x

i

+

1

)

)

.

Simpson's method of integration

Figure 1.

If the function

f

(

x

)

is continuous on

[

a

,

b

]

,

then

b

a

f

(

x

)

d

x

Δ

x

3

[

f

(

x

0

)

+

4

f

(

x

1

)

+

2

f

(

x

2

)

+

4

f

(

x

3

)

+

2

f

(

x

4

)

+

+

4

f

(

x

n

1

)

+

f

(

x

n

)

]

.

The coefficients in Simpson’s Rule have the following pattern:

1

,

4

,

2

,

4

,

2

,

,

4

,

2

,

4

,

1

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