Calculate the definite integral of f(x)=e^2x from x=0 to x=2.

The definite integral is the area which has to be found,
that is located between the given curve y = e^2x and the lines x = 0 and x = 2, also the
x axis.

To calculate the area, we'll use the
formula:

S = Integral (f(x) - ox)dx = Int f(x)dx = Int
e^(2x) dx

Int e^(2x) dx = e^(2x)/2 +
C

Now, we'll calculate the value of the area, using
Leibnitz Newton formula::

S = F(2) - F(0),
where

F(2) = e^(2*2)/2 =
e^4/2

F(0) = e^(2*0)/2 = e^0/2 =
1/2

S = e^4/2 - 1/2

S = (e^4 -
1)/2

We have a difference of squares, at
numerator:

S =
(e^2-1)(e^2+1)/2

S =
(e-1)(e+1)(e^2+1)/2