Project ForgeEngineering Mathematics
Calculus
GATE 2017
Hard
A parametric curve defined by x = cos(πu/2), y = sin(πu/2) in the range 0 ≤ u ≤ 1 is rotated about the X-axis by 360 degrees. The area of the surface generated is
- Aπ/2
- Bπ
- 2π
- D4π
Explanation
This traces a quarter-circle arc of unit radius (x²+y²=1). ds = √((dx/du)²+(dy/du)²) du = (π/2) du (constant). Surface area = ∫₀¹ 2πy ds = π² ∫₀¹ sin(πu/2) du = π²·[-2/π cos(πu/2)]₀¹ = π²·(2/π)(1-0) = 2π.
Source: GATE ME 2017 Session 1 (ME-1) (2017)
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