# Setting up an abs. value integral

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• Sep 26th 2009, 01:44 PM
HELLMACH
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.
• Sep 26th 2009, 02:18 PM
skeeter
Quote:

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

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

solve for x in both cases.

$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
$