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sicp-all-tasks/sicp/1_002e29

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Exercise 1.29: Simpson’s Rule is a more accurate
method of numerical integration than the method illustrated above. Using
Simpson’s Rule, the integral of a function
f
between
a
and
b
is
approximated as
h
3
(
y
0
+
4
y
1
+
2
y
2
+
4
y
3
+
2
y
4
+
+
2
y
n
2
+
4
y
n
1
+
y
n
)
,
where
h
=
(
b
a
)
/
n
, for some even integer
n
, and
y
k
=
f
(
a
+
k
h
)
. (Increasing
n
increases the
accuracy of the approximation.) Define a procedure that takes as arguments
f
,
a
,
b
, and
n
and returns the value of the integral, computed
using Simpson’s Rule. Use your procedure to integrate cube between 0
and 1 (with
n
=
100
and
n
=
1000
), and compare the results to those of
the integral procedure shown above.