what-is-the-area-bounded-by-the-curve-y-x-x-2-x-5-and-the-x-axis-

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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