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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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
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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