1. TRIGONOMETRIC SUBSTITUTION

2. TRIGONOMETRIC SUBSTITUTION
NOTE:
We convert the radical into a cos function
NOTE:
We remove the radical

3. TRIGONOMETRIC SUBSTITUTION

4. TRIGONOMETRIC SUBSTITUTION
In this section, we consider integrals containing radicals
Example
Find
The main idea is how to get rid of the radicals.
( use trig. Substitution)

5. TRIGONOMETRIC SUBSTITUTION

6. TRIGONOMETRIC SUBSTITUTION
triangle
domain
Identity
substitution
Expression

7. TRIGONOMETRIC SUBSTITUTION
Final061

8. TRIGONOMETRIC SUBSTITUTION

9. TRIGONOMETRIC SUBSTITUTION
Final152

10. TRIGONOMETRIC SUBSTITUTION
Expression

11. TRIGONOMETRIC SUBSTITUTION
We can transform the integrand into a function for which trigonometric substitution is appropriate by first completing the square under the root sign
substitution
Expression

13. TRIGONOMETRIC SUBSTITUTION

14. TRIGONOMETRIC SUBSTITUTION
In the following table we list trigonometric substitutions that are effective for the given radical expressions because of the specified trigonometric identities.

15. TRIGONOMETRIC SUBSTITUTION

16. TRIGONOMETRIC SUBSTITUTION

17. TRIGONOMETRIC SUBSTITUTION
Example
substitution
Expression
Find

18. TRIGONOMETRIC SUBSTITUTION
EXAM-2
Term-092

19. EXAM-2Term-102
substitution
Expression

20. TRIGONOMETRIC SUBSTITUTION
Expression
Example
Find

21. Find TRIGONOMETRIC SUBSTITUTION hyperbolic substitutions Example
can be used in place of trigonometric substitutions and sometimes they lead to simpler answers. But we usually use trigonometric substitutions because trigonometric identities are more familiar than hyperbolic identities.

22. TRIGONOMETRIC SUBSTITUTION
Because the ellipse is symmetric with respect to both axes, the total area is four times the area in the first quadrant

23. substitution
Expression

24. substitution
Expression

25. TRIGONOMETRIC SUBSTITUTION

26. TRIGONOMETRIC SUBSTITUTION