Advertisement Remove all ads

Methods of Integration: Integration by Substitution

Advertisement Remove all ads

Topics

notes

The given integral ∫f(x)dx  can be transformed into another form by changing 
the independent variable x to t by substituting x = g (t).
Consider             I =∫ f x dx   
Put x = g(t) so that `(dx)/(dt)` = g'(t)
dx = g′(t) dt
Thus   I =∫f(x) dx ∫f ( g (t))g'( t) dt 
This change of variable formula is one of the important tools available to us in the name of integration by substitution.

description

  • ∫ tan x dx = log | sec x |  + C
  • ∫ cot x dx = log | sin x | + C
  • ∫ sec x dx = log | sec x + tan x | + C
  • ∫ cosec x dx = log | cosec x – cot x | + C
If you would like to contribute notes or other learning material, please submit them using the button below.

Video Tutorials

We have provided more than 1 series of video tutorials for some topics to help you get a better understanding of the topic.

Series 1


Series 2


Series 3


Shaalaa.com | Indefinite Integration by U Substitution

Shaalaa.com


Next video


Shaalaa.com


Indefinite Integration by U Substitution [00:29:56]
S
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×