What is _ e ⁻¹ ^ e ^2 | x x | dx equal to?

Step-by-step solution

aligned & _ e⁻¹ ^ e^2 | x x | d x= _ e⁻¹ ^ e^0 - x x d x+ _ e^0 ^ e^2 x x d x & = -1 2 [( x)^2 ]_ e⁻¹ ^ e^0 + 1 2 [( x)^2 ]_ e^0 ^ e^2 & = -1 2 [0- ( e⁻¹ )^2 ]+ 1 2 [ ( e^2 )^2-0 ] & = -1 2 (-1)+ 1 2 (2)^2= 1 2 + 4 2 = 5 2 aligned