A community for students.
Here's the question you clicked on:
 0 viewing
MarcLeclair
 2 years ago
Hi, my question is more theoritical. I know how to integrate ( mostly) but I don't understand the integration process itself. I asked teachers, looked on the internet, etc... The concept that FTC 1 and FTC 2 explain. I do not understand how integrating a function gives its anti derrivative ( therefore, I'm guessing integrating means finding the area, then how does the anti derrivative define the area).
By the logic above, a change in x(or delta x ) is the sum of the infinitesimal changes dx . It is also equal to the sum of the infinitesimal products of the derivative and time. This infinit
MarcLeclair
 2 years ago
Hi, my question is more theoritical. I know how to integrate ( mostly) but I don't understand the integration process itself. I asked teachers, looked on the internet, etc... The concept that FTC 1 and FTC 2 explain. I do not understand how integrating a function gives its anti derrivative ( therefore, I'm guessing integrating means finding the area, then how does the anti derrivative define the area). By the logic above, a change in x(or delta x ) is the sum of the infinitesimal changes dx . It is also equal to the sum of the infinitesimal products of the derivative and time. This infinit

This Question is Closed

MarcLeclair
 2 years ago
Best ResponseYou've already chosen the best response.0It is also equal to the sum of the infinitesimal products of the derivative and time. This infinite summation is integration; hence, the integration operation allows the recovery of the original function from its derivative. It can be concluded that this operation works in reverse; the result of the integral can be differentiated to recover the original function

MarcLeclair
 2 years ago
Best ResponseYou've already chosen the best response.0Wikipedia explanation of the FTC and integral

Topi
 2 years ago
Best ResponseYou've already chosen the best response.0Or you could watch session 52 where FTC1 & 2 are proved.

LeventAChaves
 2 years ago
Best ResponseYou've already chosen the best response.0It is not infinity. Not all sums of infinite terms gives you an infinite numer. In fact, there are a lot of infinite sums that gives you a finite number. For example if you take \[\lim_{x \rightarrow \infty}(1+1/n)^n=e\] lets check: This expression is the sum of infinite terms but it does give us an finite number. This is one of the wonders on math. I hope that my answer proves usefully.

LeventAChaves
 2 years ago
Best ResponseYou've already chosen the best response.0And Integrals is like sum all height times base. And derivatives is like height divided by base. So you can think in terms of the same reason that make multiplication and division inverse process.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.