Integrating Reverse Chain Rule and Substitution in Calculus
I
n
t
e
g
r
a
t
i
o
n
:
R
e
v
e
r
s
e
c
h
a
i
n
r
u
l
e
o
r
s
u
b
s
t
i
t
u
t
i
o
n
Silent
Teacher
Narration
Your Turn
Intelligent
Practice
Practice
Worked Example
Your Turn
@DrChris_Baker
@DrChris_Baker
@DrChris_Baker
@DrChris_Baker
Explore the concepts of reverse chain rule and substitution in integration through worked examples and practice questions involving trigonometric functions. Enhance your skills with interactive narration and practical exercises. Dive into the world of calculus with a silent teacher guiding you through intelligent practice sessions.
Download Presentation
Please find below an Image/Link to download the presentation.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author. Download presentation by click this link. If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.
E N D
Presentation Transcript
Integration: Integration: Reverse chain rule Reverse chain rule or substitution or substitution Silent Teacher Intelligent Practice Your Turn Narration 6? ?2 43?? sin?cos??? Practice
Worked Example Your Turn ? ?2+ 12?? ?2?3+ 12?? ? ?2 ?2+ 1?? ?3+ 1?? @DrChris_Baker
2?3 ?2 3?+??? 1. ? ?2 62?? 11. 2. sin2?cos??? ? 1.5 ?2 3?+??? 12. 3. sin5?cos??? 13. 2? 3 ??2 3?+2?? 4. ?cos ?2 3 ?? 14. 2? 3 sin ?2 3? + 2 ?? 5. ?cos ?2 3 ?? 3?2 4?+3 (?3 2?2+3? 2)?? 15. 6. ?2cos ?3 3 ?? 6?2 8?+6 (?3 2?2+3? 2)?? 16. 7. ?2cos ?3 3 ?? ?2? 3 ?2? 3 2 ?? ? 17. ?2 3?? 8. 18. tan3?sec2? ?? ?2 ?3 3?? 9. 20. ???4??????2 ? ?? 2? 3 ?2 3?+2?? 10. @DrChris_Baker 21. tan???
1. sin?cos??? = 1 2cos2? + ? =1 2sin2? + ? 2. sin2?cos??? =1 3sin3? + ? 3. sin5?cos??? =1 6sin2? + ? 4. ?cos ?2 3 ?? =1 2sin(?2 3) + ? 5. ?cos ?2 3 ?? =1 2sin(?2 3) + ? 6. ?2cos ?3 3 ?? =1 3sin(?3 3) + ? 7. ?2cos ?3 3 ?? =1 3sin(?3 3) + ? 2? 3 ?2 3?+2?? = ln ?2 3? + 2 + ? ?2 3?? =1 ? 2ln|?2 3| + ? 10. 8. ?2 ?3 3?? =1 3ln|?3 3| + ? 9. @DrChris_Baker
20. ???4??????2 ? ?? = 1 5cot5? + ? 2? 3 ?2 3?+??? = ln ?2 3? + 2 + ? 11. 21. tan??? = ln sec? + ? ? 1.5 ?2 3?+??? =1 2ln ?2 3? + ? + ? 12. 13. 2? 3 ??2 3?+2?? = ??2 3?+2+ ? 14. 2? 3 sin ?2 3? + 2 ?? = cos ?2 3? + 2 + ? 3?2 4?+4 (?3 2?2+3? 2)??= ln ?3 2?2+ 3? 2 + ? 15. 6?2 8?+6 (?3 2?2+3? 2)?? = 2ln ?3 2?2+ 3? 2 + ? 16. ?2? 3 ?2? 3 2 ?? =1 2ln|?2? 3 2| + ? 17. 18. tan3?sec2? ?? =1 4tan4? + ? @DrChris_Baker
