Question

Y=x^3, x=0, x=2Рассчитать площадь фигуры с помощью интеграла​

Answer 1

Ответ:

Пошаговое объяснение:

S=ИНТ.(от 0 до2)x^3dx=x^4/ 4 |(от 0 до 2)=2^4/ 4-0=16/4=4

Answer 2

To calculate the area of the figure bounded by the curve y = x^3 and the lines x = 0 and x = 2, we can use definite integration.

The area (A) under the curve between x = 0 and x = 2 is given by the integral:

A = ∫[from 0 to 2] (x^3) dx

Let's evaluate this integral step by step:

Step 1: Find the antiderivative (integral) of x^3 with respect to x: ∫ (x^3) dx = (1/4) * x^4 + C, where C is the constant of integration.

Step 2: Evaluate the antiderivative at the limits of integration: A = (1/4) * (2^4) - (1/4) * (0^4) = (1/4) * 16 - 0 = 4

So, the area of the figure bounded by y = x^3 and the lines x = 0 and x = 2 is 4 square units.