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GATE 2020 PI – Question 45

Engineering Mathematics · Numerical Methods · 2 marks · Numerical answer

For y=−x²+9x−2, approximate $\int_1^5y\,dx$ by Simpson’s one-third rule with two intervals (two decimals).

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Correct answer: 58.00 to 59.00

Explanation

Interval width is h=(5−1)/2=2. The values at1,3,5 are6,16,18. Simpson gives(h/3)[6+4(16)+18]=(2/3)88=58.6667, or58.67. Because y is quadratic this rule is exact here.

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