Is it in the syllabus for GATE 2017?

2 votes

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

5 votes

Best answer

= 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