Using the Fundamental Teorem of Calculus: `int_(-1)^1 -e^x dx`this is what I have: -1S e^x dx = -1*(e^x+1)/(x+1) = -(e^2)/(2)-0 = -e^2/2

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You should remember the fundamental theorem of calculus for a function f(x) that is continuous over [a,b] such that:

`int_a^b f(x) dx = F(b) - F(a)`

You also need to remember that int `e^x dx = e^x + c`  such that:

`int_(-1)^1 -e^x dx = -e^x|_(-1)^1`

`int_(-1)^1 -e^x dx = -(e^1 - e^(-1))`

`int_(-1)^1 -e^x dx = e^(-1) - e`

Using the negative power identity yields:

`a^(-b) = 1/(a^b)`

Reasoning by analogy yields:

`int_(-1)^1 -e^x dx = 1/e - e => int_(-1)^1 -e^x dx = (1-e^2)/e`

Hence, evaluating the definite integral using the fundamental theorem of calculus yields `int_(-1)^1 -e^x dx = (1-e^2)/e` .