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Social ScienceUse the trapezoidal rule and Simpson's rule to approximate the value of the definite integral. Compare your result with the exact value of the integral. (Give your answers correct to 4 decimal places.) 2∫53ln(x)dx; n=4
Use the trapezoidal rule and Simpson's rule to approximate the value of the definite integral. Compare your result with the exact value of the integral. (Give your answers correct to 4 decimal places.)
2∫53ln(x)dx; n=4
Expert Answer
Evaluate the definite integral using trapezoidal rule and Simpson’s rule. And compare with exact value.
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Given: 5 J3ln (x)dx;n 4 Trapezoidal rule: b Дх Хо 2 n-1 b-a where, Ar Simpson Rule: b Дк )-re [s(*)*+4s {y)+251x2) +4s( f(x)dx 3 n-1 b-a where, Ar n
From the given information, a= 2, b= 5 and n=4.
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b-а п 5-2 Ar = 4 3 Ax = 0.75 4 End points: -2, =2+0.75 2.75 xz=2.75+0.75 =3.5 =3.5+0.75 4.25 -4.25+0.75 5 4
Substitute known...
![Trapezoidal rule:
5
In(x)dk =
2)-2s(%2)+25(ag)* S(%g)]
(2)+2 (2.75)+ 2f (3.5) +2f (4.25)+f (5)
2
31n(2)+2x3 n(2.75)+2x3 In(3.5)+2x3 In (4,25)+3 In(5)]
8
0.375 2.0794+6.0696+7.5166+8.6815+4.8283
10.9408](https://prod-qna-question-images.s3.amazonaws.com/qna-images/answer/f26bd2c7-a69a-414f-95bc-e32ed97937d0/be188390-7cb9-4caf-9e32-97b55784f48d/jvof4e7.png)
Image Transcriptionclose
Trapezoidal rule: 5 In(x)dk = 2)-2s(%2)+25(ag)* S(%g)] (2)+2 (2.75)+ 2f (3.5) +2f (4.25)+f (5) 2 31n(2)+2x3 n(2.75)+2x3 In(3.5)+2x3 In (4,25)+3 In(5)] 8 0.375 2.0794+6.0696+7.5166+8.6815+4.8283 10.9408
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