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Use Simpson's rule to approximate the following integral and compare your1.result to the exact value of the integral.6x21dx

Question
Use Simpson's rule to approximate the following integral and compare your
1.
result to the exact value of the integral.
6x21dx
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Use Simpson's rule to approximate the following integral and compare your 1. result to the exact value of the integral. 6x21dx

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check_circleAnswer
Step 1

The integral is given as

(2x -6x +1)
First simply integrate it
2
4
6
+
3
=8-16 2
=-6
Thus, the exact result of definite integral is-6
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(2x -6x +1) First simply integrate it 2 4 6 + 3 =8-16 2 =-6 Thus, the exact result of definite integral is-6

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Step 2

For Simpson’s rule, the area is approximated within two intervals

and x,x
Ax
That is, A
3
)(%.)
Forn sub intervals, the integral becomes
b-a f(a)+4f(x) + 2f (x, )+4f(x)+ 2f(x.)
...+f(x)4(x)+ f(b)
3n+.
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and x,x Ax That is, A 3 )(%.) Forn sub intervals, the integral becomes b-a f(a)+4f(x) + 2f (x, )+4f(x)+ 2f(x.) ...+f(x)4(x)+ f(b) 3n+.

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Step 3

Obtain the width of eac...

b-a 2-0
n
1
=_
2
[0,0.5].[0.5.1],11.5] and [1.5,2].
Thus, the subintervals
are
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b-a 2-0 n 1 =_ 2 [0,0.5].[0.5.1],11.5] and [1.5,2]. Thus, the subintervals are

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