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: $384\pi$