Find the area of the closed figure bounded by the following curve
$y = 3 x + 18 - x^{2}$ , $y = 0$ .

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Solution

$y = 3 x + 18 - x^{2}, y = 0$
$0 = - x^{2} + 3 x + 18$
$(6 - x) (x + 3) = 0$
$x = 6, - 3$
Area enclosed between $x = 6 a n d x = - 3 b y t h e c u r v e i s \int_{- 3}^{6} (- x^{2} + 3 x + 18 - 0)$
$[- \frac{x^{3}}{3} + 3 \frac{x^{2}}{2} + 18 x]_{- 3}^{6} = - 20 + \frac{81}{2} + 162 = 224.5 s q . u n i t s$

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