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.

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.