Evaluation of \int_{2}^{4} x^{3} d x using a 2-equal-segment trapezoidal rule gives a value of ____________

GATE Mechanical Engineering (ME) 2019 Shift 1 Solved Paper

Question : 12 of 65

Marks: +1, -0

Evaluation of

∫↙{2}↖{4} x^{3} d x

using a 2-equal-segment trapezoidal rule gives a value of ____________

Solution:

h=\;{4-2}/{2}=1

y	2	3	4
$x^3$	8	27	64

∫ y d x=\;{h}/{2}[(y_{2}+y_{4})+2(y_{3})]=\;{1}/{2}[(8+64)+2(27)]

=63

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