area using integrals

• Dec 6th 2007, 01:42 PM
cowboys111
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
• Dec 6th 2007, 03:03 PM
galactus
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.