`int_(2)^(8) |x - 5| dx` किसके बराबर है

Options

A. 2
B. 3
C. 4
D. 9

Explanation

`int_(2)^(8) |x - 5 | dx`
` = int_(2)^(5) |x - 5 | dx | int_(5)^(8) |x-5|dx`
`| :' int_(a)^(b) f(x) dx = int_(a)^(b) f(x) dx ] + int_(c)^(a) f(x) dx`
` = - int_(2)^(5) (x- 5) dx + int_(5)^(8) (x-5) dx`
` = - ((x^(2))/(2) - 5x)^(5) + [(x^(2))/(2) - 5x]_(5)^(8)`
` = - [(25/2 - 25) - (2-10) ] + [ (32-40) - ((25)/(2) - 25)]`
` = (25)/(2) - 8 - 8 + (25)/(2) = 9`