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Showing posts with label integration. Show all posts
Showing posts with label integration. Show all posts

## HOW TO LEARN INTEGRATION FORMULAE/FORMULAS USING TRICKS

Let us learn and remember most Important formulas of Integration , tips and tricks to learn algebraic ,most important differentiation questions for +2 maths, indefinite integration tricks and shortcuts trigonometric and by parts formulas in an easy and short cut manners.

## 1.   ∫ sin x dx           =  - cos x +c

where "c" is called constant of Integration.

The integration of sin x is  - cos x ,then divide it with the derivative of its angle.

If we have to find the integration of  sin 2x , then we shall find it as

Step 1.    1st find the integration of sin x which is - cos x .

Step 2.    Divide it with the derivative of 2x ,which is 2, so

∫ sin 2x dx     =  - ( cos 2x) 2 + c ,
∫ sin 8x dx      =  - ( cos 8x) 8 + c ,

∫ sin  3x4  dx  =   - ( cos  3x4 )   3 4  + c ,
Therefore   ∫ sin nx dx =  - ( cos nx) n +c ,

## 6 ∫ cosec x dx = - log |cosec x - cot x | + c

If we want to integrate cosec√x .Then 1st of all we apply the formula of integration of cosec (any angle) then formula of integration of √x, So we have

∫  cosec√x dx = - (log | cosec√x -co√x | )(2√x) + c

## 7  ∫ sec² x dx = tan x + c

Because the derivative of tan x is sec²  x , So the Anti derivative or Integration of sec² x  is tan x .

∫ sec² √x dx  =  (2√x ) tan √x  + c

∫ cosec²  dx = - cot x + c

Because the derivative of  cot x is  - cosec² x , So the  Anti derivative or Integration of  cosec 2 x is - cot x .

## 8 ∫ sec x tan x dx = sec x +c

Because the derivative of sec x is sec x tan x ,Therefore the integration of tan x sec x is sec x .

If we want to integrate sec√x .tan √x .Then its  integration  will be sec √x,

sec √x tan √x   dx      =  √x   sec √x + c

## 9 ∫ cosec x cot x dx = - cosec x + c

Because the derivative of cosec x is    - cosec x cot x , Therefore the integration of tan x sec x is sec x .

∫ cosec √x cot √x dx = - ( 2 √x  cosec √x ) +c

## Integration of constant function is the constant function itself multiplied by the variable . ∫ 5 dx   = 5x  +c

2  ∫  xn  dx  = xn+1  n+1dx  + c ,

## Conclusion

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