How do you find the volume bounded by y=sqrtxy=x and the lines y=0 and x=4 revolved about the y=-1?

1 Answer
Jun 23, 2016

(56 pi )/3 56π3

Explanation:

DesmosDesmos

the volume of a small element is given by

Delta V = pi ((1+sqrt(x))^2 - (1)^2 ) Delta x
= pi (1+2 sqrt(x) + x - 1 ) Delta x
= pi (2 sqrt(x) + x ) Delta x

So V = pi \int_0^4 \ 2 sqrt(x) + x \ dx

= pi [4/3 x^{3/2} + x^2/2 ]_0^4

= pi( [4/3 * 8 + 8 ]- 0)

= (56 pi )/3