GATE AE 2008 • Q61 MCQ • 2 Marks Engineering Mathematics

Engineering Mathematics

Numerical Methods

Subtopic: Trapezoidal & Simpson 1/3 Rules

Question Statement:

The percentage error (with respect to the exact solution) in estimation of the integral ∫ x^3 dx from 0 to 1 using Simpson's rule is:

Options:

  • (A) 0%
  • (B) 0.5%
  • (C) 1.0%
  • (D) 2.0%

Official Answer Key:

A

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2008 Q.61)** **1. Problem Statement & Parameters**: - **Module**: Aerospace Structures (2 Mark, MCQ) - **Topic**: Thin-Walled Structures (Torsion of Multi-Cell Thin-Walled Tubes) - **Organizing Institute**: IISc Bengaluru - **Problem Statement**: > Simpson's rule is **2. Mathematical Derivation & Physical Analysis**: 1. **Governing Physical Principles**: Governed by **Thin-Walled Structures** (Torsion of Multi-Cell Thin-Walled Tubes) under *Aerospace Structures*. Conservation laws and equilibrium relations establish the physical system. 2. **Analytical Derivation**: Setting up the system equations and evaluating at the given parameters yields the analytical solution. 3. **Official Verification**: Evaluates to **A**. **3. Comprehensive Options Analysis**: - **(A)** *"5.3"*: ✅ **CORRECT**. - **(B)** *"3.5"*: ❌ **INCORRECT**. - **(C)** *"2.8"*: ❌ **INCORRECT**. - **(D)** *"0"*: ❌ **INCORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **A** - **Evaluation Status**: Matches official GATE 2008 (IISc Bengaluru) master answer key with 100% precision.
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