How do you find the volume of the solid generated by revolving the region bounded by the curves $y = x^{2}$ $y=x^2$ , y=0 x=2 rotated about the x-axis?

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How do you find the volume of the solid generated by revolving the region bounded by the curves $y = x^{2}$ $y=x^2$ , y=0 x=2 rotated about the x-axis?

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Answer 1 · 2015-08-30T16:22:56

See the explanation.

Explanation:

A at a value of $x$ $x$ in $[0, 1}$ $[0,1}$ , a representative disk has radius $top y - bottom y$ $"top "y - "bottom "y$ which will be $x^{2} - 0 = x^{2}$ $x^2-0=x^2$

Th volume of a disk is $π r^{2} \cdot thickness$ $pi r^2 * "thickness"$ .

The thickness in this case is $d x$ $dx$

Volume of slice: $π {(x^{2})}^{2} d x$ $pi(x^2)^2 dx$

Volume of the solid $\int_{0}^{1} π {(x^{2})}^{2} d x$ $int_0^1 pi(x^2)^2 dx$

We need:

$π \int_{0}^{1} x^{4} d x = π {[\frac{x^{5}}{5}]}_{0}^{1}$ $piint_0^1 x^4 dx = pi [x^5/5]_0^1$

$= π [\frac{{(1)}^{5}}{5} - \frac{0^{5}}{5}]$ $= pi[(1)^5/5 - (0^5)/5]$

$= \frac{π}{5}$ $= pi/5$

The volume is $\frac{π}{5}$ $pi/5$

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How do you find the volume of the solid generated by revolving the region bounded by the curves $y = x^{2}$ $y=x^2$ , y=0 x=2 rotated about the x-axis?

1 Answer

Explanation:

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Science

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Humanities

... and beyond

How do you find the volume of the solid generated by revolving the region bounded by the curves y=x2y=x^2, y=0 x=2 rotated about the x-axis?

1 Answer

Explanation:

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How do you find the volume of the solid generated by revolving the region bounded by the curves $y = x^{2}$ $y=x^2$ , y=0 x=2 rotated about the x-axis?