GATE 2021 PI – Question 63

Engineering Mathematics · Numerical Methods · 2 marks · Numerical answer

At x = 0,1,…,10, y(x) values are 5,3,0,−5,−10,−6,0,5,11,18,30. Use the trapezoidal rule for $\int_0^{10}y(x)dx$, to one decimal.

Show answer and explanation

Correct answer: 33.4 to 33.6

Explanation

With h = 1, interior ordinates sum to 3+0−5−10−6+0+5+11+18 = 16. Therefore $I=(h/2)[y_0+y_{10}+2\sum_{i=1}^9y_i]=(5+30+32)/2=\mathbf{33.5}$.

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