integrating Absolute value of x

[refid]

I have no clue how to intergrate this one can sume help.


. . . . . Integrate: \(\displaystyle \large{\int{\,|x|dx}\) b =1 a=-1

i have tried

. . . . .Integrate: \(\displaystyle \large{\int{\,|x|dx} ={\,|x^2/2|}\)

does not work out

 

[pka]

Use the definition of absolute value:
\(\displaystyle \L
\int\limits_{ - 1}^1 {|x|dx} = \int\limits_{ - 1}^0 {-xdx + } \int\limits_0^1 {xdx}\)

 

[refid]

\(\displaystyle \L
\int\limits_{ - 1}^1 {e^{|x|}dx} = \int\limits_{ - 1}^0 {e^-^x dx + } \int\limits_0^1 {e^xdx}\)

would this be correct as well?

 

[pka]

YES!