# Thread: Setting up an abs. value integral

1. ## Setting up an abs. value integral

INSTRUCTIONS
Sketch the region enclosed by the curves and find its area:

y= 2 +|x-1|
y= -x/5 + 7

I need to find the intercepts and then solve it by splitting the limits of integration between x>0 and x>0 but how do you find the intercepts?

If this problem shows up on a test I know I won't have time or space to sketch it.

2. Originally Posted by HELLMACH
INSTRUCTIONS
Sketch the region enclosed by the curves and find its area:

y= 2 +|x-1|
y= -x/5 + 7

I need to find the intercepts and then solve it by splitting the limits of integration between x>0 and x>0 but how do you find the intercepts?

If this problem shows up on a test I know I won't have time or space to sketch it.
for $\displaystyle x \ge 1$ , $\displaystyle 2+(x-1) = -\frac{x}{5} + 7$

for $\displaystyle x < 1$ , $\displaystyle 2-(x-1) = -\frac{x}{5} + 7$

solve for x in both cases.

$\displaystyle A = \int_{-5}^1 \left(-\frac{x}{5}+7\right) - [2 - (x-1)] \, dx + \int_1^5 \left(-\frac{x}{5}+7\right) - [2 + (x-1)] \, dx$