1.

Using properties evaluate the following definite integrals, evaluate the following: int_2^8 |x-5|dx

Answer»

SOLUTION :`|X-5|` = `{ x-5, x ge 5
-(x-5), x LT 5}`
therefore `int_2^8 |x-5| dx`
=`int_2^5 (5-x)dx + int_5^8 (x-5) dx`
=`(5X-x^2/2)_2^5 + (x^2/2 -5x)_5^8`
`(25-(25)/2)-(10-4/2)+((64)/2 - 40)-((25)/2 -25)`
`(25)/2-8-8+(25)/2 = 25-16 = 9`


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