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