Notes: `xy = 1, x = 0, y = 1, y = 3` Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by...

Thursday, 22 August 2013

$\displaystyle{x}{y}={1},{x}={0},{y}={1},{y}={3}$ Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by...

The shell has the radius y, the cricumference is $\displaystyle{2}\pi\cdot{y}$ and the height is $\displaystyle\frac{{1}}{{y}}$ , hence, the volume can be evaluated, using the method of cylindrical shells, such that:

$\displaystyle{V}={2}\pi\cdot{\int_{{1}}^{{3}}}{y}\cdot{\left(\frac{{1}}{{y}}\right)}{\left.{d}{y}\right.}$

Reducing like terms yields:

$\displaystyle{V}={2}\pi\cdot{\int_{{1}}^{{3}}}{\left.{d}{y}\right.}$

$\displaystyle{V}={2}\pi\cdot{y}{{\mid}_{{1}}^{{3}}}$

$\displaystyle{V}={2}\pi\cdot{\left({3}-{1}\right)}$

$\displaystyle{V}={4}\pi$

Hence, evaluating the volume, using the method of cylindrical shells, yields $\displaystyle{V}={4}\pi.$

$\displaystyle{V}={2}\pi\cdot{\int_{{1}}^{{3}}}{y}\cdot{\left(\frac{{1}}{{y}}\right)}{\left.{d}{y}\right.}$

Reducing like terms yields:

$\displaystyle{V}={2}\pi\cdot{\int_{{1}}^{{3}}}{\left.{d}{y}\right.}$

$\displaystyle{V}={2}\pi\cdot{y}{{\mid}_{{1}}^{{3}}}$

$\displaystyle{V}={2}\pi\cdot{\left({3}-{1}\right)}$

$\displaystyle{V}={4}\pi$

Hence, evaluating the volume, using the method of cylindrical shells, yields $\displaystyle{V}={4}\pi.$

Notes

Thursday, 22 August 2013

$\displaystyle{x}{y}={1},{x}={0},{y}={1},{y}={3}$ Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by...

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Is there any personification in "The Tell-Tale Heart"?

Thursday, 22 August 2013

Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by...

No comments:

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Is there any personification in &quot;The Tell-Tale Heart&quot;?

$\displaystyle{x}{y}={1},{x}={0},{y}={1},{y}={3}$ Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by...

Is there any personification in "The Tell-Tale Heart"?