Deter. Definite Integ.?

Question

Write definite integral to rep. volume of solid formed when y=3-x^2 , y=2 revolved about y=2.

Answer 1

dV= pi*r^2 *dx where r= y-2 = 1-x^2 and x varies from
-1to +1
v= Int(-1 to +1) pi(1-x^2)^2 dx
= pi Int (1-2x^2+x^4)dx = pi(x-2/3x^3 +1/5x^5) between -1 and 1
=pi( 1-2/3+1/5 -1+2/3+1/5) = 2pi/5