Question

What is integration and fundamental formulea of integration

Answer 1

$\Huge{\sf Integration \colon}$

Integration is the process of anti differentiation

For example,

Consider x³, it's derivative would be 3x²

But now if you are want to get x³ from 3x², you integrate 3x²

Here you go,

$\displaystyle{ \sf \: l = \int \: 3 {x}^{2}.dx } \\ \\ \leadsto \: \displaystyle{ \sf l = 3 \big[ \dfrac{ {x}^{2 + 1} }{2 + 1} \big]} \\ \\ \leadsto \: \boxed { \boxed{ \sf \: l = {x}^{3} + c }}$

Arbitrary Constant

• C is referred to as Arbitrary Constant

• C is added to the end result of the integration process

• It represents all the function of the given integral

Significance Of Integration

• Integration is used to find the area under a graph.

• In physics,it helps us to find velocity from acceleration and so on

Integration is solved by using the formula :

$\displaystyle \: \sf \: l = \int \: \dfrac{ {x}^{n + 1} }{n + 1}$

Answer 2

Answer:

Integration:

it is the reverse process of differentiation...

Formulae:

$\int\limits {x^n} \, dx$=(xⁿ⁺¹)/n+1 +c

$\int\limits {} \, dx$=c

$\int\limits{sin x} \, dx$=-cos x+ c

$\int\limits {cosx} \, dx$=sin x+ c

etc

where 'c' is the constant

Hope this helps you