Question

∫|x-4|dx

Answer 1

depends on whether \(x\geq 4\) or \(x<4\)

Answer 2

between 0 and 6

Answer 3

?

Answer 4

x greater than or equal to 4, i think

Answer 5

is it really
\[\int_0^6|x-4|dx\]?

Answer 6

yes! :)

Answer 7

easy method is to draw a picture and find the area of two triangles using one half base time height

Answer 8

less easy method is to break the integral in to two pieces and compute each of them separately

Answer 9

possible answers are: 6, 8, 10 or 11

Answer 10

please help!

Answer 11

could you help me find the answer please??

Answer 12

Recall:
\[|x|=\begin{cases}x&\text{for }x\ge0\\-x&\text{for }x<0\end{cases}\]
which means
\[|x-4|=\begin{cases}x-4&\text{for }x\ge4\\4-x&\text{for }x<4\end{cases}\]
So, if you want to evaluate the integral using the second method satellite mentioned, you would have
\[\int_0^6|x-4|~dx=\int_0^4(4-x)~dx+\int_4^6(x-4)~dx\]

Answer 13

thanks!!