What is the area between f(x)=5x^4+3x^2, x=1 and x=2 ?

We notice that it 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
(5x^4+3x^2)dx

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

 Int (5x^4+3x^2)dx = Int 5x^4dx + Int
3x^2dx

Int 5x^4dx = 5x^5/5 +
C

Int 5x^4dx = x^5 + C

 Int
3x^2dx = 3*x^3/3 + C

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

Int (5x^4+3x^2)dx = x^5 + x^3 +
C

F(2) - F(1) = 2^5 + 2^3 - 1^5 -
1^3

F(2) - F(1) = 32 + 8 -
2

F(2) - F(1) =
38

The area bounded by the curve of f(x) and
the lines x=1, x=2 and x axis is A=38 square
units.