Q.3 (A) (ii) Find the area of the region bounded by the parabola y²=25x and the line x=5 .

Answer: 100√(5)/3 sq. units The parabola is symmetric about the X-axis; for the upper half y=5√(x) . Area =2∫₀⁵ 5√(x) dx=10[fracx^(3/2)3/2]₀⁵=20/3(5^(3/2))=20/3×5√(5)=100√(5)/3 sq. units.

Find the area of the region bounded by the parabola \(y^2=25x\) and the line \(x=5\).

Q.3 (A) (ii) Find the area of the region bounded by the parabola \(y^2=25x\) and the line \(x=5\).

Doubtly Asked 28 Oct 2026 Board exam · March 2025 hsc 12th Save WhatsApp Report

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Answer: \(\frac{100\sqrt{5}}{3}\) sq. units

The parabola is symmetric about the X-axis; for the upper half \(y=5\sqrt{x}\).

Area \(=2\int_0^5 5\sqrt{x}\,dx=10\left[\frac{x^{3/2}}{3/2}\right]_0^5=\frac{20}{3}\left(5^{3/2}\right)=\frac{20}{3}\times5\sqrt{5}=\frac{100\sqrt{5}}{3}\) sq. units.

Doubtly AI · 28 Oct 2026 AI-verified · Oct 2026 Report

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Find the area of the region bounded by the parabola \(y^2=25x\) and the line \(x=5\).

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