Indefinite integral

🏆Practice domain of a function

An integral can be defined for all values (that is, for all X X ). An example of this type of function is the polynomial - which we will study in the coming years.

However, there are integrals that are not defined for all values (all X X ), since if we place certain X X or a certain range of values of X X we will receive an expression considered "invalid" in mathematics. The values of X X for which integration is undefined cause the discontinuity of a function.

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Test yourself on domain of a function!


Given the following function:

\( \frac{5-x}{2-x} \)

Does the function have a domain? If so, what is it?

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  • An example of this is a function with a fraction with values X X in the denominator.
  • For example 1x1\over x
    According to mathematical rules, the denominator of a fraction cannot be zero since it is not possible to divide by zero. Therefore, when there is a possibility that the denominator equals zero, the integral cannot be defined for the values of X X that could cause the denominator to be zero.
  • Another example is a square root function. For example
    According to the algebraic rules, the expression under the square root cannot be negative, that is, it must be positive or zero, but in no way negative. Therefore, The integral will be undefined for a range of values of X X that cause the expression under the square root to be negative.f(x)=x2x5f(x)=\sqrt{x^2-x-5}

If you are interested in this article, you might also be interested in the following articles:

Graphical representation of a function

Algebraic representation of a function

Function notation

Domain of a function

Numeric value assignment in a function

Variation of a function

Increasing function

Decreasing function

Constant function

Functions for seventh grade

Intervals of increase and decrease of a function

On the Tutorela website, you will find a variety of articles with interesting explanations about mathematics

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