volume of revolution about the y-axis with more than 1 line??

Question

i can easily integrate to find volumes around the x-axis and other x lines but when it cimes to the y-axis and there is more than one line and i must find the volume betwwen when rotated i get very confused!
for example can someone guide me through this slowly- you will be greatly appreciated as i am taking as level maths in year 9 and i need all the help i can get thanx:

find the volume generated when the region bounded by them curves y=2x(squared) and y= 3-(x squared) is rotated 180 degrees about the y -axis

sorry if this is not clear

thanx connor!

Answer 1

intercept both curves
2x^2= =3-x^2 so x^2 = 1 and x=+-1
so you have two regions one for 0 2 As you rotate only 180º
V = 1/2 pi( Int (0,2)y/2dy +int (2,3) (3-y)dy =1/2*pi(1+1/2)=3/4*pi

Answer 2

hi

1) x = y/2
2) x = + √(3 -y)

cross point
y^2/4 = 3 - y
y^2 + 4 y - 12 = 0
y1= -6 (don't matter); y2 = 2

then

V = π [ int (y=2 to 3) (3-y) dy +
+ int (y=0 to 2) (y^2/4) dy ]

V = π [ ((3*3 - 3^2/2) - ( 3*2 - 2^2/2)) +
+ (2^3 / 12 - 0^3/12) ]

V = π [1/2 + 2/3]
V = 7/6 π

finally
"is rotated 180 degrees about the y -axis"

V/2 = 7/12 π

bye