# Math Help - area using integrals

1. ## area using integrals

Hi, the problem starts out by giving:
y = 2+|x-1| and y = -(1/5)x+7

the next step in the solution book takes y = 2+|x-1| and turns it into:
3-x, x<= 1
1+x, x >=1

I know that 3-x is negative and 1+x is positive but how do you figure that out?
Thank you

2. What are you to do exactly. Are you given limits of integration?.

Break the abs up into two separate integrals.

$\int_{\frac{-15}{2}}^{1}[(\frac{-1}{5}x+7)-(-x+1)]dx+\int_{1}^{\frac{10}{3}}[(\frac{-1}{5}x+7)-(x+3)]dx$

EDIT: Oops, looks like I mistakenly used 2+|x+1| instead of 2+|x-1|. You get the idea. Adjust accordingly.