Find the volume of the body obtained by rotation about the Ox axis of the function y = x ^ 2 and x = 0, x = 3.
| August 2, 2021 | education
The volume of a body of revolution, if the dependence of the change in its cross-sectional area is known, is determined by the formula:
V = integral (a to b) f (x) dx.
Because the area of the spherical section is pi * R², then we get the function:
f (x) = pi * R² = pi * (x²) ² = pi * x4.
Therefore, the volume of the body of revolution will be equal to:
V = integral (from 0 to 3) pi * x4 dx = pi * x ^ 5/5 (from 0 to 3) = pi * 3 ^ 5/5 = 48.6 * pi units ³.
Answer: the volume of the body is 48.6 * pi units ³.
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