Indefinite integral - Examples, Exercises and Solutions

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.

Suggested Topics to Practice in Advance

  1. Ways to represent a function
  2. Representing a Function Verbally and with Tables
  3. Graphical Representation of a Function
  4. Algebraic Representation of a Function
  5. Notation of a Function
  6. Rate of Change of a Function
  7. Variation of a Function
  8. Rate of change represented with steps in the graph of the function
  9. Rate of change of a function represented graphically
  10. Constant Rate of Change
  11. Variable Rate of Change
  12. Rate of Change of a Function Represented by a Table of Values
  13. Functions for Seventh Grade
  14. Increasing and Decreasing Intervals (Functions)
  15. Increasing functions
  16. Decreasing function
  17. Constant Function
  18. Interval of decrease of the function
  19. Increasing Intervals of a function

Practice Indefinite integral

Exercise #1

Given the following function:

5x2x \frac{5-x}{2-x}

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

Video Solution

Answer

Yes, x2 x\ne2

Exercise #2

Given the following function:

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

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

Video Solution

Answer

Yes, x4 x\ne-4

Exercise #3

Given the following function:

5x \frac{5}{x}

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

Video Solution

Answer

Yes, x0 x\ne0

Exercise #4

Given the following function:

235x2 \frac{23}{5x-2}

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

Video Solution

Answer

Yes, x25 x\ne\frac{2}{5}

Exercise #5

Given the following function:

9x4 \frac{9x}{4}

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

Video Solution

Answer

No, the entire domain

Exercise #1

Look at the following function:

2x+202x10 \frac{2x+20}{\sqrt{2x-10}}

What is the domain of the function?

Video Solution

Answer

x > 5

Exercise #2

Consider the following function:

3x+42x1 \frac{3x+4}{2x-1}

What is the domain of the function?

Video Solution

Answer

x12 x\ne\frac{1}{2}

Exercise #3

Look at the following function:

2x+23x1 \frac{2x+2}{3x-1}

What is the domain of the function?

Video Solution

Answer

x13 x\ne\frac{1}{3}

Exercise #4

Given the following function:

128x4 \frac{12}{8x-4}

What is the domain of the function?

Video Solution

Answer

x12 x\ne\frac{1}{2}

Exercise #5

Look at the following function:

5x+24x3 \frac{5x+2}{4x-3}

What is the domain of the function?

Video Solution

Answer

x34 x\ne\frac{3}{4}

Exercise #1

Look at the following function:

10x35x3 \frac{10x-3}{5x-3}

What is the domain of the function?

Video Solution

Answer

x35 x\ne\frac{3}{5}

Exercise #2

Look the following function:

15x4 \frac{1}{5x-4}

What is the domain of the function?

Video Solution

Answer

x45 x\ne\frac{4}{5}

Exercise #3

Given the following function:

2421x7 \frac{24}{21x-7}

What is the domain of the function?

Video Solution

Answer

x13 x\ne\frac{1}{3}

Exercise #4

Look at the following function:

2x+29x+6 \frac{2x+2}{9x+6}

What is the domain of the function?

Video Solution

Answer

x23 x\ne-\frac{2}{3}

Exercise #5

Look at the following function:

2010x5 \frac{20}{10x-5}

What is the domain of the function?

Video Solution

Answer

x12 x\ne\frac{1}{2}

Topics learned in later sections

  1. Domain of a Function
  2. Inputing Values into a Function