Calculate the area of the figure bounded by the lines y = 2x squared, y = 0, x = 2.

univerkov | September 18, 2021 | education

Let’s calculate the area of the figure bounded by the lines:

y = 2 * x ^ 2;

y = 0;

x = 2.

S = (-1 to 2) ∫ 2 * / x ^ 2 / dx = (-1 to 2) (2 * x ^ (2 + 1) / 3) = (-1 to 2) (2 * x ^ 3/3) = (-1 to 2) (2/3 * x ^ 3) = 2/3 * 2 ^ 3 – 2/3 * (-1) ^ 3 = 2/3 * 8 – 2 / 3 * (-1) = 2 * 8/3 + 2/3 * 1 = 16/3 + 2/3 = (16 + 2) / 3 = 18/3 = 6;

Answer: S = 6.

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