GATE ME 2020 Set 1 — Question 36
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Engineering Mathematics → Numerical Methods → Trapezoidal & Simpson's Rules
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Question
The evaluation of the definite integral by using Simpson's 1/3rd (one-third) rule with step size yields
Correct answer
(D) 0.592
Solution
With on there are sub-intervals (even, so Simpson's 1/3 rule applies).Let :
(The exact value is ; Simpson's rule is not exact here because has a kink at .)
- (A) 0.914 and (B) 1.248 do not correspond to this rule (1.248 is , i.e. ignoring the sign of for ).
- (C) 0.581 is the exact integral, not the Simpson estimate.
- (D) 0.592 is the Simpson's 1/3 rule value.
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