Exams › GATE › Engineering Mathematics

Match the CORRECT pairs. Numerical Integration Scheme | Order of Fitting Polynomial P. Simpson's 3/8 Rule | 1. First Q. Trapezoidal Rule | 2. Second R. Simpson's 1/3 Rule | 3. Third

1. P-2, Q-1, R-3
2. P-3, Q-2, R-1
3. P-1, Q-2, R-3
4. P-3, Q-1, R-2

Correct answer: P-3, Q-1, R-2

Solution

Simpson's 3/8 Rule fits a cubic polynomial, which corresponds to a third-order approximation, while the Trapezoidal Rule fits a linear polynomial (first order), and Simpson's 1/3 Rule fits a quadratic polynomial (second order). This matching aligns with the characteristics of each numerical integration scheme.

Related GATE Engineering Mathematics questions

• The smallest positive root of the equation x⁵ - 5x⁴ - 10x³ + 50x² + 9x - 45 = 0 lies in the range
• For a flowing fluid, a dimensionless combination of velocity (V), length scale (l), and acceleration due to gravity (g) would be
• The second derivative of a function f is computed using the fourth-order Central Divided Difference method with a step length h. The CORRECT expression for the second derivative is
• In the IEEE floating point representation the hexadecimal value 0x00000000 corresponds to
• Let r denote number system radix. The only value(s) of r that satisfy the equation √121_r = 11_r, is/are
• The Newton-Raphson iteration xₙ₊₁ = 1/2 (xₙ + R/xₙ) can be used to compute the

⚔️ Practice GATE Engineering Mathematics free + battle 1v1 →