GATE BT 2021 • Q59
NAT • 2 Marks
Section 1: Engineering Mathematics
Calculus
Subtopic: Fundamentals of Calculus
Question Statement:
Calculate the following integral
I sin vi do =
Step-by-Step Solution & Explanation
### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2021 Q.59)**
**1. Governing Concept & Definition**:
- **Topic**: Engineering Mathematics & Definite Integrals
- Integration of sinusoidal function over a half-cycle $[0, \pi]$:
$\int_0^\pi \sin x \, dx = [-\cos x]_0^\pi$
**2. Detailed Step-by-Step Calculation**:
- **Evaluation**:
$[-\cos \pi] - [-\cos 0] = -(-1) - (-1) = 1 + 1 = 2$
**3. Final Answer**:
- **Calculated Value**: **2**
- **Official GATE Accepted Range**: **2 to 2**
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