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# As Maths

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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.

Nov 25, 2017

#1
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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

Nov 25, 2017
edited by Mr.Owl  Nov 25, 2017
#2
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For powers of x, we have:

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

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Nov 26, 2017
#3
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It is not just divide by (power + 1) and add 1 to the power.

Examples:

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

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Nov 27, 2017