use the trapezoidal rule ,the midpoint rule and simpson's rule to approximately the given integral with the specified value of n .
when n=10
Answers
Answer:
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Answer:
The parameters for approximating the given definite integral are given by:
n
=
4
,
Δ
x
=
π
2
−
0
4
=
π
8
,
a
=
0
and
b
=
π
2
Let us assume that
f
(
x
)
=
3
√
2
+
cos
(
x
)
Now:
Dividing the given interval
[
0
,
π
2
]
into
n
=
4
sub-intervals of length
Δ
x
=
π
8
, we get the following endpoints:
0
,
π
8
,
π
4
,
3
π
8
and
π
2
By using the Trapezoidal Rule, the approximate value of the given definite integral is:
T
4
=
π
16
[
f
(
0
)
+
2
f
(
π
8
)
+
2
f
(
π
4
)
+
2
f
(
3
π
8
)
+
f
(
π
2
)
]
=
π
16
[
3
√
2
+
cos
(
0
)
+
2
3
√
2
+
cos
(
π
8
)
+
2
3
√
2
+
cos
(
π
4
)
+
2
3
√
2
+
cos
(
3
π
8
)
+
3
√
2
+
cos
(
π
2
)
]
≈
2.163916
Step-by-step explanation:
hope it will help you