Question

Для функции f(x)=-2cosx найдите первообразных, график которой проходит через точку А(п/6;3) Помогите пожалуйста!!!!!

Answer 1

Всё подробно написала в решении.

Answer 2

Finding the Antiderivative of f(x) = -2cos(x)

To find the antiderivative of the function f(x) = -2cos(x), we can use the basic integration rules for trigonometric functions. The antiderivative of cos(x) is sin(x), and since we have a coefficient of -2 in front of cos(x), the antiderivative of -2cos(x) is -2sin(x).

Therefore, the antiderivative of f(x) = -2cos(x) is F(x) = -2sin(x) + C, where C is the constant of integration.

Finding the Graph Passing Through Point A(pi/6, 3)

To find the graph of the antiderivative F(x) = -2sin(x) + C that passes through the point A(pi/6, 3), we can substitute the x-coordinate and y-coordinate of point A into the equation and solve for the constant of integration C.

Given that the x-coordinate is pi/6 and the y-coordinate is 3, we have the following equation:

3 = -2sin(pi/6) + C

Using the trigonometric identity sin(pi/6) = 1/2, we can simplify the equation:

3 = -2 * (1/2) + C 3 = -1 + C

Solving for C, we find:

C = 4

Therefore, the equation of the graph passing through point A(pi/6, 3) is F(x) = -2sin(x) + 4.

Graph of the Antiderivative Passing Through Point A(pi/6, 3)

To visualize the graph of the antiderivative passing through point A(pi/6, 3), we can plot the function F(x) = -2sin(x) + 4 on a graph.

Here is a graph of the function F(x) = -2sin(x) + 4:


Please note that the graph is a rough representation and may not be to scale. It is always recommended to use graphing software or a graphing calculator for accurate and precise graphs.

I hope this helps! Let me know if you have any further questions.