what is the area bounded by the curve y=x(x−2)(x−5) and the x axis?


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Question Number 207938 by necx122 last updated on 31/May/24

$w h a t i s t h e a r e a b o u n d e d b y t h e c u r v e$ $y = x (x - 2) (x - 5) a n d t h e x a x i s ?$
	Answered by mr W last updated on 31/May/24

	$A = \int_{0}^{2} x (x - 2) (x - 5) d x - \int_{2}^{5} x (x - 2) (x - 5) d x$ $= {[\frac{x^{4}}{4} - \frac{7 x^{3}}{3} + 5 x^{2}]}_{0}^{2} - {[\frac{x^{4}}{4} - \frac{7 x^{3}}{3} + 5 x^{2}]}_{2}^{5}$ $= 2 \times [\frac{2^{4}}{4} - \frac{7 \times 2^{3}}{3} + 5 \times 2^{2}] - [\frac{5^{4}}{4} - \frac{7 \times 5^{3}}{3} + 5 \times 5^{2}]$ $= \frac{253}{12}$
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