Find the area bounded by curve \(x^2 + y = 0\), X-axis and lines \(x = 1\) and \(x = 4\).
Q.12 Find the area bounded by curve \(x^2 + y = 0\), X-axis and lines \(x = 1\) and \(x = 4\).
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Answer: 21 sq. units
The curve is \(y = -x^2\), which lies below the X-axis, so the area is the absolute value of the integral.
Area \(= \left|\int_{1}^{4}(-x^2)\,dx\right| = \left[\frac{x^3}{3}\right]_{1}^{4} = \frac{64 - 1}{3} = 21\) sq. units.
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· 28 Oct 2026
AI-verified · Oct 2026
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