Project ForgeEngineering Mathematics
Calculus
GATE 2017
Medium
P(0,3), Q(0.5,4), and R(1,5) are three points on the curve defined by f(x). Numerical integration is carried out using both the Trapezoidal rule and Simpson's rule within limits x=0 and x=1 for the curve. The difference between the two results will be
- 0
- B0.25
- C0.5
- D1
Explanation
The three given points (0,3), (0.5,4), (1,5) are exactly collinear (f increases by 2 for every unit of x). Both the trapezoidal rule and Simpson's rule are exact for a linear (degree ≤ 1) integrand, so both give the same (exact) result, and their difference is 0.
Source: GATE ME 2017 Session 1 (ME-1) (2017)
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