Question

ПервообразнЫМИ функции y= (2x-7)^9 являются: 1. 1/20(2x-7)^10 2. 1/10(2x-7)^10+9 3. 18*(2x-8)^8-3 4. 1/20(2x-7)^10 - 35 Одну нашла, ответ 1. Но есть еще,понять не могу какие

Answer 1

1/20(2х-7)^10+C
Поэтому ответы 1 и 4
1) С=0
4) С= -35

Answer 2

Pervobytnye Functions of y = (2x-7)^9

The primitive functions of the function y = (2x-7)^9 are:

1. 1/20(2x-7)^10 2. 1/10(2x-7)^10 + C, where C is the constant of integration 3. 18*(2x-8)^8 - 3 + C, where C is the constant of integration 4. 1/20(2x-7)^10 - 35 + C, where C is the constant of integration

The first primitive function is indeed 1/20(2x-7)^10. However, there are additional primitive functions, which include the constant of integration, denoted by + C. This constant arises from the indefinite integral and represents the family of functions that differ by a constant value.

The primitive function of a given function is not unique, and it is essential to include the constant of integration when finding the primitive function.

Is there anything else you would like to know about primitive functions or calculus in general?