Answer: the volume V generated by rotating the regions 281.49
Step-by-step explanation:
Given that;
the radius of the shell ⇒ (4 - x)
then the circumference of the shell is 2π( 3 - x ) i.e 2π × radius
y = 0 and x = 2
the height of the shell is 3x⁴
Now the volume of the solid obtained by rotating
the bounded region about x = 4 is;
V = ²∫₀ 2π ( 4 - x ) ( 3x⁴ ) dx
= ²∫₀ 2π ( 12x⁴ - 3x⁵ ) dx
= 2π [ 12x⁵/5 - 3x⁶/6 ]₀² {BY FTC -2]
= 2π [ (12×32)/5 - (3×64)/6 ] - ( 0-0) ]
= 2π [ 76.8 - 32]
= 2π [ 44.8 ]
= 281.49
Therefore the volume V generated by rotating the regions 281.49
