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in Co-ordinate geometry by (50 points)
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Area bounded between the curves y = |x2 - 9| and overline y = 3 is equal to :

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1 Answer

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∴ Area = \(\int\limits^{\sqrt{12}}_{-\sqrt6} y \, dx\)

\(= \int\limits^0_{-\sqrt6} -(x^2 - 9)dx + \int\limits_0^{\sqrt{12}}(x^2 - 9)dx\)

\(= - \left[\frac{x^3}3 - 9x\right]^0_{-\sqrt6} + \left(\frac{x^3}3 - 9x\right)^{\sqrt{12}}_0\)

\(= \frac{-6\sqrt6}3 + 9\sqrt6 + \left|\frac{12\sqrt{12}}{3}- 9\sqrt{12}\right|\)

\(= - 2\sqrt6 + 9\sqrt6 + | 4\sqrt{12} - 9\sqrt{12}|\)

\(= 7\sqrt6 + 5\sqrt{12}\)

\( = 7\sqrt6 + 10\sqrt3 \) square units.

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