help!! intergration using sub Watch

This discussion is closed.
flaminchocolate
Badges: 0
Rep:
?
#1
Report Thread starter 13 years ago
#1
i just dont get it!!! i was ill when they went through it in the lesson so ive no idea what its about!! i tried reading the text book but it just gave me a headach basically i need to help how to do it than explaining what it is or when to use it. thanks guys!!!
0
m:)ckel
Badges: 2
Rep:
?
#2
Report 13 years ago
#2
Example 8 from P3 Book (Edexcel) - P111.

Use the substitution u=cosx to find INT(tanx)dx

INT tanx dx = INT (sinx/cosx) dx

Now, we have to find a way to substitute 'u' into this.

We know that u = cosx

If we're gonna use 'u', we have to change to 'dx' to something in terms of 'du' (since we now want to integrate with respect to u).

So, we differentiate the substitution given:

du/dx = -sinx
Rearrange to make dx the subject: dx = -du/sinx

Now sub in all that you have into the original integral:

INT (sinx/cosx)dx = INT (sinx/u)(-du/sinx) . . . since u=cosx, and dx = -du/sinx

The sinx's cancel, to give:

INT (-1/u)du

= -ln(u) + c

But, u = cosx

So you get: INT (tanx) dx = -ln(cosx) + c
0
flaminchocolate
Badges: 0
Rep:
?
#3
Report Thread starter 13 years ago
#3
thanks!!
0
X
new posts
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

University open days

  • University of the Arts London
    MA Performance Design and Practice Open Day Postgraduate
    Thu, 24 Jan '19
  • Brunel University London
    Undergraduate Experience Days Undergraduate
    Sat, 26 Jan '19
  • SOAS University of London
    Postgraduate Open Day Postgraduate
    Sat, 26 Jan '19

Are you chained to your phone?

Yes (68)
19.54%
Yes, but I'm trying to cut back (143)
41.09%
Nope, not that interesting (137)
39.37%

Watched Threads

View All