Question

What is the total area of the regions between the curves y = 6x2 − 18x and y = −6x from x = 1 to x=3?.

Answer 1

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:

$A = \int_{x = a}^{x = b} |f(x) - g(x)| dx$

In this problem, we have that:

$f(x) = 6x^2 - 18x, g(x) = -6x, a = 1, b = 3$.

Hence, the area is:

$A = \int_{1}^3 |6x^2 - 12x| dx$

$A = |x^3 - 6x^2|_{x = 1}^{x = 3}$

Applying the Fundamental Theorem of Calculus:

$A = |3^3 - 54 - 1^3 + 6|$

$A = 22$

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 brainly.com/question/20733870