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.
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.
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)
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.
The graph of $\displaystyle y \:=\:|2x +3|$ looks like this:Code:| | / | / | / 3|/ * /| / | - -*- + - - - / | / |
And we are to evaluate from 0 to 2.Code:| | / | * | /: | / : 3|/ : \ * : \ /| : \ / | : -*- + - + - - | 2 |
(We could have ignored the absolute values!)