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file: GATE CH 2020 (with Solutions).pdf

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Consider the following data se t./x1351525 f ( x)6 8 12 5 10/rd

²⁵()

Calculate the value of f ( x )dx by Simpson 1/3 method _______.

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Simpson 1/3 method

ₐ^ᵇf(x)

dx = h{/3(y_0+y_n)+4(y_1+y_3+−−−−−+y_n)+2(y_2+y_4+−−−−+y_n_{−}_2)} /text{Where}

h = ((b-a) {/frac{/frac{)}{nh} /text{represents} /text{equal} /text{interval} b}{w} b /text{and} a}_1^{25} f (x))

dx = ₁^5f(x)dx+₅^{25}f(x)dx

⇒h = /frac{(5-1)}{2} = 2

⇒h = /frac{(25-5)}{2} = 10

₁^5f(x)

dx = h{/3(y_0+y_n)+4(y_1)+2(0)} = 2{/36+10+4 /times 8+2 /times 0} = /frac{2}{3} /times 48 = 32

₅^{25}f(x)

dx = h{/3(y_0+y_n)+4(y_1)+2(0)} = 10{/310+5+4 /times 12+2 /times 0} = /frac{10}{3} /times 63 = 210

∴ Adding this two integral :

25f(x)dx = 32+210 = 2421

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Source PDF: GATE CH 2020 (with Solutions).pdf

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