Can anyone define integration?

I am not sure if its divide the expression by the power and increase the power of x by 1 or not.

Rauhan
Nov 25, 2017

#1**+1 **

Integration Definitions:

1.

The action or process of integrating.

2. In mathamatics:

The finding of an integral or integrals.

If that did not answer your question then look at this page for a more mathamatical explanation:

http://mathsfirst.massey.ac.nz/Calculus/integration/basics/definition.html

Mr.Owl
Nov 25, 2017

#2**+2 **

For powers of x, we have:

\(\int{x^n}dx=\frac{x^{n+1}}{n+1}\text{ as long as }n\ne-1\)

.

Alan
Nov 26, 2017

#3**+1 **

It is not just divide by (power + 1) and add 1 to the power.

Examples:

\(\displaystyle\int\cos x dx = \sin x + C\\ \displaystyle\int \sec^2 x dx = \tan x + C\\ \text{OR even more complicated:}\\ \displaystyle\int \sqrt[3]{\tan x}dx = -\dfrac{1}{2}\ln|1+\tan^{2/3}x|+\dfrac{1}{4}|\tan^{4/3}x-\tan^{2/3}x + 1|+\dfrac{\sqrt{3}}{2}\arctan\left(\dfrac{2\tan^{2/3}x-1}{\sqrt3}\right) + C\)

MaxWong
Nov 27, 2017