Question
Asked Dec 3, 2019
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Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral. (Give your answers correct to 4 decimal places.)

 

485/ln(x) dx; n=6

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Expert Answer

Step 1

Given:

5
[a,b]=[4,8]andn= 6
In (x
(x)
Subintervals of length Ar:
8-4 4
b-a
2
Ar =
6
6 3
п
The endpoints of the subintervals are:
20 22 8 b
14 16
,6,
3 3
3 3
a=4,
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5 [a,b]=[4,8]andn= 6 In (x (x) Subintervals of length Ar: 8-4 4 b-a 2 Ar = 6 6 3 п The endpoints of the subintervals are: 20 22 8 b 14 16 ,6, 3 3 3 3 a=4,

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Step 2

Use the trapezoidal rule and Simpson's rule to approximate the value

Trapezoidal:

T Ar(x) 2f (x,)+2f(x.)+2f(x,)+ 2f(x,)+2f(x,)+ f
22
16
+2f
3
4)222/(6)
20
1
Т.
2
2
+f (8)
3
+ 2f (6)+2f
+2f
=-X-
-
3
5
= 3.60673760222241
In (4
f(x) = f(a) f(4)
14
10
2f (x)2f
3
= 6.49163049260846
14
In
3
16
2f(x) 2f
10
= 5.97379974977518
16
In
3
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T Ar(x) 2f (x,)+2f(x.)+2f(x,)+ 2f(x,)+2f(x,)+ f 22 16 +2f 3 4)222/(6) 20 1 Т. 2 2 +f (8) 3 + 2f (6)+2f +2f =-X- - 3 5 = 3.60673760222241 In (4 f(x) = f(a) f(4) 14 10 2f (x)2f 3 = 6.49163049260846 14 In 3 16 2f(x) 2f 10 = 5.97379974977518 16 In 3

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Step 3

Step 2 as fo...

10
= 5.58110626551247
In (6)
2f (x;) = 2f(6)=
20
10
2f (x,) = 2f
3
= 5.27114788714934
20
In
3
22
10
2f (x,) = 2f
5.01899648841888
22
In
3
3
= 2.40449173481494
In(8)
f(x,) = f(b) = f (8) =
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10 = 5.58110626551247 In (6) 2f (x;) = 2f(6)= 20 10 2f (x,) = 2f 3 = 5.27114788714934 20 In 3 22 10 2f (x,) = 2f 5.01899648841888 22 In 3 3 = 2.40449173481494 In(8) f(x,) = f(b) = f (8) =

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