Question

What are the most fundamental methods of integration and why?

Answer 1

it,s like, so yu can drive a car, but can u reverse it?

Answer 2

You do not understand what I am asking.

Answer 3

i dont get it, sorry,

Answer 4

It is okay. The question is very broad.

Answer 5

u substitution, integration by parts, partial fractions, trig substitution,
also if you start with a function and take its derivative you know its antiderivative (original function)

Answer 6

The above fails to explain why these are the most fundamental or explain how the list is exhaustive. You are going somewhere, though.

Answer 7

\[\int x^n = {x^{n+1} \over n + 1}\]I actually find it the most fundamental because it shows that differentiation is the inverse of integration and vice-versa. Also, this is what we (mostly) start with in integration.

Answer 8

To be fully accurate, it is through the second fundamental theorem of Calculus that we can derive that \(\int dx\) and \(\frac{d}{dx}\) are inverse operators.

Answer 9

http://mathworld.wolfram.com/FundamentalTheoremsofCalculus.html

Answer 10

I never knew there was a second one to the fundamental theorem list too :/

Answer 11

The first shows that the definite integral can be expressed in terms of the indefinite integral. The second shows that integration and differentiation are inverse operators on continuous functions.

Answer 12

Wait. The fundamental theorem I knew of was that integration is the same as finding the area under a curve!

Answer 13

That's the definition of integration.

Answer 14

There are many, many definitions.