# Thread: Integration Involving Absolute Value

1. ## Integration Involving Absolute Value

How does one integrate a function involving an absolute value?

Here are two sample questions:

Let INT = integrate

(1) INT |2x-3| dx

(2) INT |2x+3| dx

For question 2, the lower limit of integration is 0 and the upper limit of integration is 2.

2. ## Re: Integration Involving Absolute Value

just break it into pieces using the appropriate, non absolute value, expression for the different intervals needed.

for example |x| is -x on (-infinity, 0] and x on [0, infinity)

|2x - 3| is (3 - 2x) on (-infinity, 1.5), and (2x - 3) on (1.5, infinity)

3. ## Re: Integration Involving Absolute Value

Hello, nycmath!

The problem is rather silly.

$\displaystyle (2)\;\int^2_0 |2x+3|\,dx$

The graph of $\displaystyle y \,=\,2x+3$ looks like this.

Code:
          |
|   /
|  /
| /
3|/
*
/|
/ |
- -*- + - - -
/   |
/    |
The graph of $\displaystyle y \:=\:|2x +3|$ looks like this:

Code:
          |
|    /
|   *
|  /:
| / :
3|/  :
\     *   :
\   /|   :
\ / |   :
-*- + - + - -
|   2
|
And we are to evaluate from 0 to 2.
(We could have ignored the absolute values!)

4. ## Re: Integration Involving Absolute Value

From 0 to 2 forms a trapezoid.