Posted by **Anonymous** on Thursday, December 9, 2010 at 1:10pm.

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 x-axis.

- Calculus -
**MathMate**, Thursday, December 9, 2010 at 5:45pm
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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