Find the area between f(x) = 3x^2 + 2x and x= 1 and x= 2

Since there is not established the other boundary curve,
we'll suppose that we have to calculate the area between f(x), the lines x=1 and x=2 and
the x axis.

The definite integral will be calculated with
Leibniz-Newton formula:

Int f(x)dx =
F(b)-F(a)

We'll calculate the indefinite integral of
f(x):

Int f(x)dx = Int (3x^2 +
2x)dx

We'll use the property of integral to
be additive:

 Int (3x^2 + 2x)dx = Int 3x^2dx + Int
2xdx

 Int 3x^2dx = 3*x^3/3 +
C

Int 3x^2dx =x^3 + C

Int 2xdx
= 2*x^2/2 + C

Int 2xdx = x^2 +
C

 Int (3x^2 + 2x)dx = x^3 + x^2 +
C

F(2) - F(1) = 2^3 + 2^2 - 1^3 -
1^2

F(2) - F(1) = 8 + 4 -
2

F(2) - F(1) =
10

The area bounded by the curve of f(x) and
the lines x=1, x=2 and x axis is A=10.