Question

How do you integrate absolute value functions?

Answer 1

divide into the two cases where \(f(x)>0\) and where \(f(x)<0\)

Answer 2

You split the absolute value equation into two equations?

Answer 3

an example would be great

Answer 4

Integrate them by breaking them into parts, one from where the function is positive originally, and the other by applying a negative sign to that part of the limits where the function is negative ('cause the graph is flipped from that point)

Answer 5

\[\int_{-1}^5|x-3|dx=\int_{-1}^3(3-x)dx+\int_3^5(x-3)dx\] for example

Answer 6

easy example since
\[f(x) = |x-3| = \left\{\begin{array}{rcc}
3-x & \text{if} & x <3 \\
x-3& \text{if} & x \geq 3
\end{array}
\right.\]

Answer 7

What about 2x from -2 to 4?

Answer 8

@Romero Do you mean integration of |2x| from -2 to 4??

Answer 9

Well year we are talking about absolute values here right?

Answer 10

From here we see that we will have to integrate from -2 to 0 with the equation-1/2 x
and 2x from 0 to 4
Note how we inversed the slope.

Answer 11

wait..why is it when x is greater than or less than 3

Answer 12

|x−3|

Answer 13

Well, in that case it is
\[2 \int\limits_{-2}^{4} |x|\]

f(x) = x for x > 0
= - x for x<0

Substituting this we get.

\[2 \int\limits_{-2}^{0} (-x) + 2 \int\limits_{0}^{4} x\]

rest you can solve :)