Homework Help: Calculus

Posted by Mike on Tuesday, May 10, 2011 at 5:14pm.

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

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