Question

Знайти ПЕРВІСНУ функції: 1) f(x)=8x+π2) f(x)=8x³-33) f(x)=1+sinx​

Answer 1

1)F(x)=8x²/2+πx+c==4x²+πx+c

2) F(x)=8x⁴/4-3x+c=2x⁴-3x+c

3)F(x)=x-cosx​+c

Answer 2

Finding the Original Functions

Let's find the original functions for the given derivatives.

1. Finding the Original Function for f(x) = 8x - The original function for f(x) = 8x is obtained by integrating the derivative with respect to x. The integral of 8x with respect to x is 4x^2 + C, where C is the constant of integration.

2. Finding the Original Function for f(x) = 8x³-3 - The original function for f(x) = 8x³-3 is obtained by integrating the derivative with respect to x. The integral of 8x³-3 with respect to x is 2x^4 - 3x + C, where C is the constant of integration.

3. Finding the Original Function for f(x) = 1+sinx - The original function for f(x) = 1+sinx is obtained by integrating the derivative with respect to x. The integral of 1+sinx with respect to x is x - cosx + C, where C is the constant of integration.

Therefore, the original functions for the given derivatives are: 1. f(x) = 4x^2 + C 2. f(x) = 2x^4 - 3x + C 3. f(x) = x - cosx + C

These are the original functions corresponding to the given derivatives.