Respuesta :
Using integration, it is found that the area between the two curves is of 22 square units.
What is the area between two curves?
The area between two curves y = f(x) and y = g(x), in the interval from x = a to x = b, is given by:
[tex]A = \int_{x = a}^{x = b} |f(x) - g(x)| dx[/tex]
In this problem, we have that:
[tex]f(x) = 6x^2 - 18x, g(x) = -6x, a = 1, b = 3[/tex].
Hence, the area is:
[tex]A = \int_{1}^3 |6x^2 - 12x| dx[/tex]
[tex]A = |x^3 - 6x^2|_{x = 1}^{x = 3}[/tex]
Applying the Fundamental Theorem of Calculus:
[tex]A = |3^3 - 54 - 1^3 + 6|[/tex]
[tex]A = 22[/tex]
The area between the two curves is of 22 square units.
More can be learned about the use of integration to find the area between the two curves at https://brainly.com/question/20733870
