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Find the volume of the solid of revolution generated by revolving the region bounded by y = 2x^2, y = 0, and x = 2 about the x-axis.

Sagot :

abidemiokin

Answer:

[tex]128 \pi/5 units^3[/tex]

Step-by-step explanation:

The volume of the solid revolution is expressed as;

[tex]V = \int\limits^2_0 {\pi y^2} \, dx[/tex]

Given y = 2x²

y² = (2x²)²

y² = 4x⁴

Substitute into the formula

[tex]V = \int\limits^2_0 {4\pi x^4} \, dx\\V =4\pi \int\limits^2_0 { x^4} \, dx\\V = 4 \pi [\frac{x^5}{5} ]\\[/tex]

Substituting the limits

[tex]V = 4 \pi ([\frac{2^5}{5}] - [\frac{0^5}{5}])\\V = 4 \pi ([\frac{32}{5}] - 0)\\V = 128 \pi/5 units^3[/tex]

Hence the volume of the solid is [tex]128 \pi/5 units^3[/tex]

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