Final answer:
To find the volume of the solid generated by revolving the region bounded by the curve and lines about the line x = -1, we can use the method of cylindrical shells.
Step-by-step explanation:
To find the volume of the solid generated by revolving the region bounded by the curve and lines about the line x = -1, we can use the method of cylindrical shells. We will integrate the volume of each shell from x = 0 to the x-coordinate where y = 4 (the intersection point of y = 4*sqrt(x) and y = 4). The radius of each shell is given by the difference between x and -1, and the height of each shell is given by the function y = 4*sqrt(x). The integral of the volume of each shell will give us the total volume.
We can set up the integral as follows:
V = ∫(2π(4*√(x))(x-(-1)))dx
Simplifying, we get:
V = 8∫(x*√(x)+√(x))dx
To evaluate this integral, we can use u-substitution. Let's let u = √(x), then du = (1/2√(x))dx. Substituting these values in, we get:
V = 8∫(2u^3+u)du
Evaluating this integral will give us the volume of the solid generated by revolving the region about the line x = -1.