Question

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves about the give line. (a) Graph the region (b) Graph the solid (c) Sketch a typical shell. (d) Determine the variable of integratoin (e) Draw and label the radius and height of the shell. Describe their length. (f) Find the volume.

y = 4x, y = 0, x = 2; revolve about the line x = -3

Answer 1

we are given equations as

revolve about the line

(a) , (b), (c)

Graph :

we can draw graph

(d)

Since,

It revolves about the line x = -3

and we can use shell method

so, variable of integration =x

(e)

(f)

Bound is from 0 to 2

we can use formula

now, we can solve each integrals

and then combine them

...........Answer