Find the surface area of the body formed by the rotation of the figure bounded by the lines y = sin2x, y = 0,0.

univerkov | July 8, 2021 | education

The surface area of the body formed by the rotation of the figure bounded by the lines y = sin2x, y = 0, 0 <x <n / 2 around the Ox axis, can be found using a definite integral:

integral from 0 to n / 2 (sin2x) = -1/2 * cos2x | from 0 to n / 2 = -1/2 * cos (2 * n / 2) – (-1/2) * cos (2 * 0) = -1/2 * cos (n) + 1/2 * cos (0) = -1/2 * (-1) + 1/2 * 1 = 1/2 + 1/2 = 1.

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