# GATE2013-23

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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 $f(x)$ 0 0.09 0.36 0.81 1.44 2.25 3.24 4.41 5.76 7.29 9

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

= 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

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Is it in the syllabus for GATE 2017?
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Numerical methods are not in GATE syllabus.
1 vote
(D) 9.045

Area under curve is f(x)

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