1. The volume of the solid obtained by rotating the region bounded by the given curves about the y-axis is given by:
V = 2π ∫0 5y (5y - y3) dy
= 2π ∫0 5y (5y2 - y4) dy
= 2π [5y3/3 - y5/5]|0 5y
= 2π [125/3 - 125/5]
= 250π/15
2. The volume of the solid obtained by rotating the region bounded by the given curves about the y-axis is given by:
V = 2π ∫0 18x-6x2 (18x-6x2) dx
= 2π ∫0 18x2 - 6x4 dx
= 2π [18x3/3 - 6x5/5]|0 18x-6x2
= 2π [54 - 54/5]
= 108π/5
1. Find the volume formed by rotating the region enclosed by x=5y and x=y^3 with y is greater than or equal to 0 about the y-axis.
2. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis y=18x-6x^2 , y=0 : about the y-axis.
PLease can anyone help me find the volume plz show ur works if u can so i can understand it better.
1 answer
2 answers