y=19x^2 y=0
Find the volume V of this solid
1 Answer

y = 1 – 9x^2
y = 0
finding limits:
1 – 9x^2 = 0
1 = 9x^2
(1/9) = x^2 =====> x = +/ (1/3)
about xaxis
A (x) = π ( outer radius )^2 – π ( inner radius )^2
A (x) = π ( 1 – 9x^2 )^2 – π ( 0 )^2
A (x) = π ( 1 – 18x^2 + 81x^4 )
(1/3)
∫ π [ ( 1 – 18x^2 + 81x^4 ) ] dx
(1/3)
. . .. .. . . .. . . . . . . … . . . (1/3)
π [ x – 6x^3 + (81/5)x^5 ) ]
. . .. . .. . . . . . .. .. . .. . . .(1/3)
π [ [ 1/3 – (1/3) ] – 6 [ (1/3)^3 – (1/3)^3 ] + (81/5) [ (1/3)^5 – (1/3)^5 ) ]
π [ [ 1/3 + (1/3) ] – 6 [ (1/27) – (1/27) ] + (81/5) [ (1/243) – (1/243) ) ]
π [ 2/3 – 6 [ (1/27) + (1/27) ] + (81/5) [ (1/243) + (1/243) ) ]
π [ 2/3 – 6 [ (2/27) ] + (81/5) [ (2/243) ]
π [ 2/3 – (12/27) + (2/5) ]
π (28/45)