Question

Найти F(x) если дано F'(x)=1-3x?

Answer 1

F(x)= x-1,5x^2 первообразная

Answer 2

To find F(x) given that F'(x) = 1 - 3x, you need to perform integration. Recall that the derivative of a function represents the rate of change of the function with respect to the independent variable, and integration is the reverse process that finds the original function from its derivative.

To integrate F'(x) = 1 - 3x with respect to x, you need to find F(x) such that:

F'(x) = d/dx[F(x)] = 1 - 3x

To find F(x), integrate the right-hand side of the equation with respect to x:

∫(1 - 3x) dx

The integral of 1 with respect to x is x, and the integral of -3x with respect to x is -3x^2/2. So, the integral of F'(x) is:

F(x) = x - 3x^2/2 + C

where C is the constant of integration. This constant is arbitrary and arises during the integration process. It represents an unknown value that we cannot determine solely from the given derivative F'(x) = 1 - 3x.

Therefore, the final expression for F(x) is:

F(x) = x - 3x^2/2 + C