Question

ntegrate |x| dx from x=-1 to 1

ans=1

HOw?

Answer 1

Break up the intergralby remembering the definition of absolue value:\[\left| x \right|=x\] if x>0
\[\left| x \right|=-x\] if x<0
\[\int\limits_{-1}^{1}\left| x \right|dx=\int\limits_{-1}^{0}(-x)dx+\int\limits_{0}^{1}xdx\]
can you handle it from here?