GATE 2017 ME (ME1) – Question 39

Engineering Mathematics · Probability and Statistics: Probability, conditional probability, sampling theorems · 2 marks · Multiple choice

P(0,3), Q(0.5,4) and R(1,5) lie on y = f(x). Integrate from x = 0 to 1 using both trapezoidal and Simpson rules. The difference between the results is

0
0.25
0.5
1

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Show answer and explanation

Correct answer: (A) 0

Explanation

With spacing $h=0.5$, the composite trapezoidal estimate is $I_T=(h/2)[3+2(4)+5]=4$. Simpson’s estimate is $I_S=(h/3)[3+4(4)+5]=4$. Their difference is zero, A. The three points lie on a straight line, which both rules integrate exactly.

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