Evaluate _ -2 ^1 f(x) d x , where f(x)= cases 1-2 x, & x 0 1+2 x, & x 0 cases

Step-by-step solution

array rl _ -1 ^1 f(x) d x= _ -1 ^0 & f(x) d x+ ₀^1 f(x) d x & = _ -1 ^0(1-2 x) d x+ ₀^1(1+2 x) d x & = [x-x^2 ]_ -1 ^0+ [x+x^2 ]₀^1 array =-(-1-1)+[1+1]=2+2=4