Q.1 (A) (iv) The area of the region bounded by the curve y=x² and the line y=4 is A. 32/3 sq. units B. 64/3 sq. units C. 16/3 sq. units D. 64 sq. units

Answer: A. 32/3 sq. units Answer: (a) 32/3 sq. units The curve meets y=4 at x=±2 . By symmetry about the Y-axis, Area =2∫₀²(4-x²)dx=2[4x-x³/3]₀²=2(8-8/3)=32/3 sq. units.

The area of the region bounded by the curve \(y=x^2\) and the line \(y=4\) is

Q.1 (A) (iv) The area of the region bounded by the curve \(y=x^2\) and the line \(y=4\) is

A. \(\frac{32}{3}\) sq. units

B. \(\frac{64}{3}\) sq. units

C. \(\frac{16}{3}\) sq. units

D. 64 sq. units

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

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Answer: A. \(\frac{32}{3}\) sq. units

Answer: (a) \(\frac{32}{3}\) sq. units

The curve meets \(y=4\) at \(x=\pm2\). By symmetry about the Y-axis,

Area \(=2\int_0^2(4-x^2)dx=2\left[4x-\frac{x^3}{3}\right]_0^2=2\left(8-\frac{8}{3}\right)=\frac{32}{3}\) sq. units.

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

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The area of the region bounded by the curve \(y=x^2\) and the line \(y=4\) is

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