Learning integration, and have gotten to a certain point. What is the next logical step?

Course Queries Syllabus Queries 3 years ago

3.97K 2 0 0 0

User submissions are the sole responsibility of contributors, with TuteeHUB disclaiming liability for accuracy, copyrights, or consequences of use; content is for informational purposes only and not professional advice.

Answers (2)

Post Answer
profilepic.png
manpreet Tuteehub forum best answer Best Answer 3 years ago

 

I've learnt the following in terms of integration;

  • What are integrals, and what do they represent?
  • Indefinite integrals as the opposite of derivatives
  • Using the power rule for derivatives to provide the power rule for integration
  • Integral as infinite sum
  • Area under curve, and area between two curves
  • Volume of solid of revolution
  • Integration by substitution
  • Integration by parts
  • Integration by partial fraction expansion
  • Improper integrals

I'm wondering where to go from here. I know the basics of numerical methods, and the fundamental theorem as well. I'm looking to go further in terms of analytical integration, but I don't know which topic would be next. Any ideas?

EDIT: I've checked the syllabus for AB/AP calculus, but it only lists very vague ideas of the concepts, and not sub-topics.

0 views
0 shares

profilepic.png
manpreet 3 years ago

Maybe it would be nice to see some stuff with complex numbers, after line integrals. For example, we can simplify some calculations, using eix=cosx+isinxeix=cos⁡x+isin⁡x. How can you calculate excosxdx∫excos⁡xdxwithout integration by parts? Is there an easy way to find an expression for the nn-th derivative of exsinxexsin⁡x? What means to differentiate a function in CC? Can we derivate something like x2y+iyxx2y+iyx? And so on. I hope this motivates you a bit (:


0 views   0 shares

No matter what stage you're at in your education or career, TuteeHUB will help you reach the next level that you're aiming for. Simply,Choose a subject/topic and get started in self-paced practice sessions to improve your knowledge and scores.

Similar Forum