Q.1 (C)(iii) Area of the region bounded by y = x⁴, x = 1, x = 5 and the X-axis will be ____.

Answer: 3124/5 sq. units (= 624.8 sq. units) y = x⁴ ≥ 0, so area = displaystyle∫₁⁵ x⁴ dx = [x⁵/5]₁⁵ = (3125 - 1)/5 = 3124/5 sq. units.

Area of the region bounded by \(y = x^4\), \(x = 1\), \(x = 5\) and the X-axis will be ____.

Q.1 (C)(iii) Area of the region bounded by \(y = x^4\), \(x = 1\), \(x = 5\) and the X-axis will be ____.

Doubtly Asked 29 Oct 2026 Board exam · July 2024 hsc 12th Save WhatsApp Report

Best answer

Answer: \(\dfrac{3124}{5}\) sq. units (= 624.8 sq. units)

\(y = x^4 \ge 0\), so area \(= \displaystyle\int_1^5 x^4\,dx = \left[\frac{x^5}{5}\right]_1^5 = \frac{3125 - 1}{5} = \frac{3124}{5}\) sq. units.

Doubtly AI · 29 Oct 2026 AI-verified · Nov 2026 Report

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