Calculus
posted by Anonymous .
Find the volume of the solid formed by rotating the region enclosed by
x=0, \ x=1, \ y=0, \ y= 8 +x^{2}
about the xaxis.

Calculus 
MathMate
The solid will be rotated about the xaxis, so we can apply the disk method by which vertical slices of thickness dx are integrated.
Radius of each slice
= y(x)
Volume of each slice
= πr²dx
= πy(x)²dx
Total volume can be obtained by integrating from x=0 to 1
V=∫ πy(x)²dx
=∫ π (8+x²)² dx
=∫ π (64+16x+x²)dx
=π [64x + 8x² + x³/3] x=0 to 1
=π[64+8+1/3]
=217π/3
Check my work.
Respond to this Question
Similar Questions

Calculus
1. Find the volume formed by rotating the region enclosed by x=5y and x=y^3 with y¡Ý0 about the yaxis. 2. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis y=18x6x^2 … 
calculus edit
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 yaxis. 2. Find the volume of the solid obtained by rotating the region bounded by the given curves about the … 
Calculus
This problem set is ridiculously hard. I know how to find the volume of a solid (integrate using the limits of integration), but these questions seem more advanced than usual. Please help and thanks in advance! 1. Find the volume of … 
Calculus II
Find the volume of the solid formed by rotating the region enclosed by x=0, x=1, y=0,y= 6 +x^{8} about the yaxis. 
CALCULUS:)
Find the volume of the solid formed by rotating the region enclosed by x=0, x=1, y=0, y=9+x^4 about the xaxis. 
Calculus :)
Find the volume of the solid formed by rotating the region enclosed by y=e^(3x)+2, y=0, x=0, x=0.4 about the xaxis. 
Calculus
a) Find the volume formed by rotating the region enclosed by x = 6y and y^3 = x with y greater than, equal to 0 about the yaxis. b) Find the volume of the solid obtained by rotating the region bounded by y = 4x^2, x = 1, and y = 0 … 
calculus
Find the volume of the solid formed by rotating the region enclosed by y=e^(2x)+1, y=0, x=0,x=0.9 about the yaxis. 
calculus
Find the volume of the solid formed by rotating the region enclosed by y=e^(2x)+1 y=0 x=0 x=0.9 about the yaxis. 
calculus
Find the volume of the solid formed by rotating the region enclosed by y=e^(2x)+1 y=0 x=0 x=0.9 about the yaxis.