Question

Find the definite integral from 0 to 5 of |8x-8|dx

Answer 1

I believe this is going to be a piece wise functions

Answer 2

Mmm yah that sounds right :) gotta split it up into pieces.

Answer 3

\[\Large\rm |8x-8|=8|x-1|\]So at x=1 we have some stuff going on.
Remember what the graph of \(\Large\rm |x|\) looks like?

Answer 4

I is a V shape

Answer 5

Ok good good good.
So this is what's happening with our function.
It's shifted one to the right, and stretched by a bit.

Answer 6

Looking at the slants gives us a better idea of what's going on.
The left branch is the negative slope portion.

Answer 7

okay!

Answer 8

Set up two integrals to find the area under these lines.
One from 0 to 1,
the other from 1 to 5.

Understand how to set those up using this information? :o