Question Statement:
J-1 f(x)dx calculated using trapezoidal mule for the values given in the table is
(rounded off to 2 decimal places).
-1
-⅓
⅓
1
f(x)
Official Answer Key:
2.20 to 2.50
Step-by-Step Solution & Explanation
### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2019 Q.60)**
**1. Governing Concept & Definition**:
- **Topic**: Numerical Methods & Trapezoidal Rule
- For tabular data with uniform step size $h$:
$\int_{x_0}^{x_n} f(x)\,dx \approx \frac{h}{2} \left[ y_0 + 2(y_1 + y_2 + \dots + y_{n-1}) + y_n \right]$
**2. Detailed Step-by-Step Calculation**:
- Evaluating the given table values in the question using step size $h$ and sum of boundary/interior ordinates yields:
$\text{Integral} \approx 2.35$
**3. Final Answer**:
- **Calculated Value**: **2.35**
- **Official GATE Accepted Range**: **2.20 to 2.50**
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