Answer to Question #166119 in Calculus for aa

Question

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the y -axis.

y =   3 x ² , y =  0, x =   4

Answer 1

Shell method formula:

$$\int_a^b2\pi xf(x)dx$$

where:

$$f(x)=3x^2, a = 0, b = 4\\$$

Then:

$$\int_0^42\pi x*3x^2dx=6\pi\int_0^4x^3dx=1.5\pi x^4\mid_0^4 =384\pi$$

Answer: $384\pi$