Project ForgeEngineering Mathematics
Calculus
GATE 2019
Medium
A parabola x = y² with 0≤x≤1 is bounded by the curve, the x-axis is the axis of symmetry, and the region between the curve and the line x=1 is shaded. The volume of the solid of revolution obtained by rotating the shaded area by 360° around the x-axis is
- Aπ/4
- π/2
- Cπ
- D2π
Explanation
Using the disk method: V = ∫₀¹ π y² dx. Since x=y², y²=x, so V = ∫₀¹ π x dx = π[x²/2]₀¹ = π/2.
Source: GATE ME 2019 Session 1 (Set 1) (2019)
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