Final answer:
To find the volume of the functions around y = -3, you need to integrate the difference between the two functions multiplied by the differential of x from the lower bound to the upper bound.
Step-by-step explanation:
The volume of the function f(x) = 3x³ and g(x) = 4x around y = -3 can be calculated using the formula for the volume of a solid of revolution. To find the volume, we need to integrate the difference between the two functions multiplied by the differential of x from the lower bound to the upper bound. In this case, the lower bound is the x-coordinate where the functions intersect, and the upper bound is the x-coordinate where the functions intersect again. Once we have the limits, we can set up the integral to find the volume:
Volume = ∫[lower bound]^[upper bound] (π((g(x))^2 - (f(x))^2))dx
Solving for the limits and performing the integration will give us the volume of the functions around y = -3.