Find V(x- x^2, [-1,2]) and V(cos(4(pie)x),[0,1]).
V(x- x^2, [-1,2])= V(x- x^2, [-1,0])+V(x- x^2, [0,1])+V(x- x^2, [1,2])=
0+0+2=2
V(cos(4(pie)x),[0,1])= 1+1=2
I was a little confused about finding the variation of a monotone function but can anyone please tell me if I found the total variations for both functions or did i go wrong at some point?
V(x- x^2, [-1,2])= V(x- x^2, [-1,0])+V(x- x^2, [0,1])+V(x- x^2, [1,2])=
V(x- x^2, [-1,0])=(-1 - (-1)^2) + (0- 0^2)= (-1-1)+0= -2
V(x- x^2, [0,1])= (0- 0^2) + (1 - 1^2) = 0 + 0 = 0
V(x- x^2, [1,2])= (1 - (1^2) + (2- 2^2)= 0+(2-4) = -2
-2+0+-2 = -4
So, now I got different answers. I dont know what I am doing wrong.