Interpreting in terms of area: int [0, 18] [ | x - 9 | ] dx

[insanerp]

Hello,

I am having trouble getting the intergal with limits of 18 and 0 of | x-9|dx

i do the intergal of x-9 =x^2/2-9x, but I can find any thing in the text book that deal with absolute values.
Can anyone help me?

Thanks,
Michele

 

[insanerp]

Re: Interpreting in terms of area

I figured it by drawing a graph

 

[tkhunny]

Re: Interpreting in terms of area

It is for you to deal with the absolute values.

This is what you need.
\(\displaystyle \int_{0}^{18}f(x)dx\;=\;\int_{0}^{9}f(x)dx\;+\;\int_{9}^{18}f(x)dx\)

And maybe this:

|x-9| = x-9 for x>= 9
|x-9| = 9-x fox x < 9

 

[skeeter]

Re: Interpreting in terms of area

I figured it by drawing a graph

... which is most probably the smartest method to use in this particular case.