Math, asked by Trinika7692, 9 months ago

Solve integration 0 to pi by 2 sinx dx by using Simpson's one third rule taking 6-subinterval

Answers

Answered by meenuraina81
1

Answer:

To approximate the Integral

b

a

f

(

x

)

d

x

using trapezoidal approximation with

n

intervals.

In this question we have:

f

(

x

)

=

sin

x

{

a

,

b

]

=

[

0

,

π

]

, and

n

=

10

.

So we get

Δ

x

=

b

a

n

=

π

0

10

=

π

10

The endpoints of the subintervals are found by beginning at

a

=

0

and successively adding

Δ

x

=

π

10

to find the points until we get to

x

n

=

b

=

π

.

x

0

=

0

,

x

1

=

π

10

,

x

2

=

2

π

10

,

x

3

=

3

π

10

. . .

x

9

=

9

π

10

, and

x

10

=

10

π

10

=

10

=

b

Now apply the formula (do the arithmetic) for

f

(

x

)

=

sin

x

.

T

4

=

Δ

x

2

[

f

(

x

0

)

+

2

f

(

x

1

)

+

2

f

(

x

2

)

+

2

f

(

x

9

)

+

f

(

x

10

)

]

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