The correct option is B 1/6 ∫_2^3|x^2 5x+6|dx #10; ∫_2^3 (+x^2 5x+6)dx #10; [ x^33∫_2^3 5 ( x^22 #10; )∫_2^3+6(x)∫_2^3] #10; [ 9 ...

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Reduction Formulae

∫23|x2-5x+6|d...

Question

$\int_{2}^{3} | x^{2} - 5 x + 6 | d x =$

1/6

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2/3

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4/7

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3/7

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Solution

The correct option is B 1/6
$\int_{2}^{3} | x^{2} - 5 x + 6 | d x$
$\int_{2}^{3} - (+ x^{2} - 5 x + 6) d x$
$- [\frac{x^{3}}{3} \int_{2}^{3} - 5 (\frac{x^{2}}{2}) \int_{2}^{3} + 6 (x) \int_{2}^{3}]$
$- [9 - \frac{8}{3} - 5 (\frac{9}{2} - 2) + 6]$
$- [9 - \frac{8}{3} - \frac{45}{2} + 10 + 6]$
$= - [\frac{- 1}{6}] = \frac{1}{6}$

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