Question

Find the following integral analytically.

Answer 1

\[\int\limits_{0}^{5} \left| 3x-9 \right| dx\]

Answer 2

Is it 39/2?

Answer 3

Yes, it is.

Answer 4

\[|3x-9|=\begin{cases}3x-9&\text{if $3x-9\ge0$}\\
-(3x-9)&\text{if $3x-9<0$}\end{cases}=\begin{cases}3x-9&\text{if $x\ge3$}\\
9-3x&\text{if $x<3$}\end{cases}\]
\[\int_0^5|3x-9|\;dx=\int_0^3(9-3x)\;dx+\int_3^5(3x-9)\;dx\]