Evaluate the following integral.
4
ex dx
1
Solution
The function
f(x) = ex
is continuous everywhere, and we know that an antiderivative is
F(x) = ex,
so part two of the fundamental theorem of calculus gives the following.
4
1
ex dx = F(4) - F(1) =
Notice that part two of the fundamental theorem of calculus says we can use any antiderivative F of f, so we may as well use the simplest one, namely
F(x) = ex,
instead of
ex + 7
or
ex + C.