# Calculus

Find the volume of the solid formed by rotating the region enclosed by
x=0, \ x=1, \ y=0, \ y= 8 +x^{2}

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1. 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.

= 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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posted by MathMate

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