Indefinite integral - Examples, Exercises and Solutions

An integral can be defined for all values (that is, for all $X$). 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 $X$), since if we place certain $X$ or a certain range of values of $X$ we will receive an expression considered "invalid" in mathematics. The values of $X$ for which integration is undefined cause the discontinuity of a function.

Practice Indefinite integral

Exercise #1

Given the following function:

$\frac{5-x}{2-x}$

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

Answer

Yes, $x\ne2$

Exercise #2

Given the following function:

$\frac{49+2x}{x+4}$

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

Answer

Yes, $x\ne-4$

Exercise #3

Given the following function:

$\frac{5}{x}$

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

Answer

Yes, $x\ne0$

Exercise #4

Given the following function:

$\frac{23}{5x-2}$

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

Answer

Yes, $x\ne\frac{2}{5}$

Exercise #5

Given the following function:

$\frac{9x}{4}$

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

Answer

No, the entire domain

Exercise #1

Look at the following function:

$\frac{2x+20}{\sqrt{2x-10}}$

What is the domain of the function?

x > 5

Exercise #2

Consider the following function:

$\frac{3x+4}{2x-1}$

What is the domain of the function?

Answer

$x\ne\frac{1}{2}$

Exercise #3

Look at the following function:

$\frac{2x+2}{3x-1}$

What is the domain of the function?

Answer

$x\ne\frac{1}{3}$

Exercise #4

Given the following function:

$\frac{12}{8x-4}$

What is the domain of the function?

Answer

$x\ne\frac{1}{2}$

Exercise #5

Look at the following function:

$\frac{5x+2}{4x-3}$

What is the domain of the function?

Answer

$x\ne\frac{3}{4}$

Exercise #1

Look at the following function:

$\frac{10x-3}{5x-3}$

What is the domain of the function?

Answer

$x\ne\frac{3}{5}$

Exercise #2

Look the following function:

$\frac{1}{5x-4}$

What is the domain of the function?

Answer

$x\ne\frac{4}{5}$

Exercise #3

Given the following function:

$\frac{24}{21x-7}$

What is the domain of the function?

Answer

$x\ne\frac{1}{3}$

Exercise #4

Look at the following function:

$\frac{2x+2}{9x+6}$

What is the domain of the function?

Answer

$x\ne-\frac{2}{3}$

Exercise #5

Look at the following function:

$\frac{20}{10x-5}$

What is the domain of the function?

Answer

$x\ne\frac{1}{2}$