Posted by Anonymous on Thursday, December 9, 2010 at 1:10pm.
The solid will be rotated about the x-axis, 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.
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