Find the area between the curve 3x^2-4x and the lines x=1 and x=2.

The area between the curve 3x^2 - 4x and the lines x=2 and
x=1 is the definite integral for the curve between 1 and
2.

Let us determine the
integral.

==> F = Int (3x^2 - 4x) dx = Int (3x^2 dx
- Int 4x dx

==> F = 3x^3/3 - 4x^2/2 +
C

==> F = x^3 - 2x^2 +
C

Now we will determine F(1) and
F(2).

==> F(1) = 1-2 +c = -1 +
C

==> F(2) = 8 - 8 + c =
c

==> Then the area is given by
:

A = F(2) - F(1) = c -(-1+c) =
1

Then the area between the curve and the
lines is 1 square units.