posted by Mike on .
True or false.
1. If F'(x) = G'(x) on the interval [a,b] then F(b)-F(a) = G(b)-G(a).
I think it's true but I just want to check my reasoning. F'(x) = G'(x) means that F(x) and G(x) differ by a constant (which may be 0). When the subtraction is done to find the definite integral this constant disappears so the statement is true.
2. True or false.
Integrate from -2(the number on the bottom of the integral) to 2 (number on the top of the integral) x^-2dx = -x^-1 = -(2)^-1-(-(-2)^-1) = (-1/2)-(1/2) = -1
I think this is false, but I'm not sure why.
Thanks for your help