Question

Для функции y=2cosx найдите первообразную,график которой проходит через точку (П/2;24)

Answer 1

Y=2cosx
F' = 2sinx + c
24 = 2sinП/2 + c
24 = 2 + c
c = 22
F' = 2sinx + 22

Answer 2

Finding the Antiderivative for y = 2cos(x)

To find the antiderivative of the function y = 2cos(x), we can use the following steps:

1. The antiderivative of cos(x) is sin(x). 2. The antiderivative of a constant multiplied by a function is the constant multiplied by the antiderivative of the function.

Using these steps, the antiderivative of y = 2cos(x) is:

F(x) = 2sin(x) + C

Where C is the constant of integration.

Finding the Value of the Constant (C)

To find the value of the constant (C), we can use the given point (π/2, 24) through which the graph of the antiderivative passes.

Substituting x = π/2 and y = 24 into the antiderivative equation, we get:

2sin(π/2) + C = 24

Solving for C:

2*1 + C = 24 C = 24 - 2 C = 22

The Antiderivative with the Given Point

Therefore, the antiderivative of y = 2cos(x) with the graph passing through the point (π/2, 24) is:

F(x) = 2sin(x) + 22

This is the function whose graph passes through the point (π/2, 24).