Math Problem Statement

Найдите первообразную функции f(x) = √3

Solution

The problem asks to find the antiderivative (or indefinite integral) of the function f(x)=3f(x) = \sqrt{3}. Let's solve it.

Solution:

The function f(x)=3f(x) = \sqrt{3} is a constant. The antiderivative of a constant cc is given by: cdx=cx+C\int c \, dx = c x + C where CC is the constant of integration.

For f(x)=3f(x) = \sqrt{3}, the antiderivative is: 3dx=3x+C\int \sqrt{3} \, dx = \sqrt{3} x + C

Final Answer:

F(x)=3x+CF(x) = \sqrt{3} x + C

Would you like further explanation or examples on antiderivatives?


Here are 5 related questions to deepen understanding:

  1. What is the antiderivative of f(x)=5f(x) = 5?
  2. How do you compute the antiderivative of f(x)=3x2+4x+1f(x) = 3x^2 + 4x + 1?
  3. Can you explain the difference between definite and indefinite integrals?
  4. How would you find the antiderivative of f(x)=exf(x) = e^x?
  5. What is the general rule for finding the antiderivative of a power function xnx^n?

Tip: Always remember to include the constant of integration CC when finding indefinite integrals!

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Math Problem Analysis

Mathematical Concepts

Calculus
Integration
Antiderivatives

Formulas

∫ c dx = cx + C

Theorems

Basic Integration Rules

Suitable Grade Level

Grades 10-12