GATE2013-23

Question

Function $f$ is known at the following points:

$x$	0	0.3	0.6	0.9	1.2	1.5	1.8	2.1	2.4	2.7	3.0
$f(x)$	0	0.09	0.36	0.81	1.44	2.25	3.24	4.41	5.76	7.29	9.00

The value of $\int_{0}^{3} f(x) \text{d}x$ computed using the trapezoidal rule is

(A) 8.983 (B) 9.003 (C) 9.017 (D) 9.045

Answer 1

= Δx/2(f(0) + 2(f(0.3) + .... + f(2.7)) + f(3.0))

= 0.15(0 + 2(0.09 + 0.36 + 0.81 + 1.44 + 2.25 + 3.24 + 4.41 + 5.76 + 7.29) + 9.00)

= 9.045

http://tutorial.math.lamar.edu/Classes/CalcII/ApproximatingDefIntegrals.aspx

Comments

Is it in the syllabus for GATE 2017?

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Numerical methods are not in GATE syllabus.

Answer 2

(D) 9.045

Area under curve is f(x)