GATE (TF) Textile 2015 Question Paper Solution | GATE/2015/TF/38

Question 38 (Textile Engineering & Fibre Science)

Let $f:[1,4] \to \mathbb{R}$ be a continuous function such that $f(1)=0.32, f(2)=0.125, f(3)=0.025$ and $f(4)=0.05$ . The value of the integral $\int_{1}^{4}f(x)dx$ , accurate up to three decimal places, obtained by Trapezoidal rule with $n=3$ is __0.335__.

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We shall prepare row column on the basis of date given-

	f(1)	f(2)	f(3)	f(4)
x	1	2	3	4
y	0.32	0.125	0.025	0.05
	Yo	Y1	Y2	Y3

By Trapezoidal rule-
f(x)= $\frac{h}{2} \times [(y_o+y_3)+2(y_1+y_2)]$
h=(4-1)/3 given n=3
h=1
f(x)= $\frac{1}{2} \times [(0.32+0.05)+2(0.125+0.025)]$
f(x)= $\frac{1}{2} \times [0.37+2(0.15)]$
f(x)= $\frac{1}{2} \times [0.37+0.3]$
f(x)= $\frac{1}{2} \times 0.67$
f(x)=0.335 (Ans)

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