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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]