GATE_AE_2027_MOCK_04_Q39
GATE 2027 Aerospace Engineering All-India Master Mock 04 (Aerospace Structures, Thin-Walled Beams & Aeroelasticity)
NAT · 2 Marks
Engineering Mathematics • Numerical Methods • Numerical Linear Algebra & Integration
Evaluate the integral I = \int_0^2 (x^3) dx using Simpson's 1/3 rule with 2 equal subintervals (h = 1.0).
Answer Key:
4
Step-by-Step Verified Solution
### Solution: f(0) = 0, f(1) = 1, f(2) = 8. Simpson's 1/3 rule with h = 1: I = (h/3) * [f(0) + 4 f(1) + f(2)] = (1/3) * [0 + 4(1) + 8] = (1/3) * 12 = 4. (Exact integral is [x^4/4]_0^2 = 16/4 = 4; Simpson's 1/3 rule is exact for cubics). Correct: 4.