GATE Questions & Answers of Integration By Simpson’s Rule

P (0,3), Q (0.5, 4), and R (1, 5) are three points on the curve defined by $\style{font-family:'Times New Roman'}{f(x)}$. Numerical integration is carried out  using both Trapezoidal rule and Simpson's rule within limits x=0 and x=1 for the curve. The difference between the two results will be

•  (A) 0
•  (B) 0.25
•  (C) 0.5
•  (D) 1

The integral $\int\limits_1^3\frac1xdx$ when evaluated by using Simpson’s 1/3 rule on two equal subintervals each of length 1, equals

•  (A) 1.000
•  (B) 1.098
•  (C) 1.111
•  (D) 1.120

Torque exerted on a flywheel over a cycle is listed in the table. Flywheel energy (in J per unit cycle) using Simpson’s rule is

•  (A) 542
•  (B) 993
•  (C) 1444
•  (D) 1986