The Student Room Group
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>

C4 help: Integrate 2sec^2xtanx

Doing C4 trig, any idea how you would you integrate this? Thanks!

Scroll to see replies

use the identity sin^2x+cos^2x=1 to find an expression for sec^2x, tan^2x and 1, substitute in for sec^2x
Reply 2
Avatar for delta-T
delta-T
OP
5
Original post by alevelstresss
use the identity sin^2x+cos^2x=1 to find an expression for sec^2x, tan^2x and 1, substitute in for sec^2x


Thanks
So you get 2(1+tan^2x) tanx?
Then 2+ 2tan^2x tanx??

Is this right, if so where from there?
i would make it 2sec^2x + 2sec^tanx and then integrate seperately
Original post by delta-T
Doing C4 trig, any idea how you would you integrate this? Thanks!


Alternative, much simpler method - think about what the derivative of tanx is and how that is relevant.
The answer is (Tanx)^2 + c
yeah it is actually just tan^2x, as its where you have f(x)f'(x)
Reply 7
Avatar for B_9710
B_9710
18
Consider derivative of (tanx)^2 .
Reply 8
Avatar for delta-T
delta-T
OP
5
Original post by alevelstresss
yeah it is actually just tan^2x, as its where you have f(x)f'(x)


Original post by Rafoleeno
The answer is (Tanx)^2 + c

image.jpeg
Apparently it's sec^2x??
Original post by delta-T
image.jpeg
Apparently it's sec^2x??


crap yeah sorry my heads messed up

its because with sec^2x you differentiate as 2secx times the derivative of sec x which is sec x tan x

so d(sec^2x)/dx is 2secxsecxtanx or 2sec^2xtanx

sorry haha
Original post by alevelstresss
crap yeah sorry my heads messed up

its because with sec^2x you differentiate as 2secx times the derivative of sec x which is sec x tan x

so d(sec^2x)/dx is 2secxsecxtanx or 2sec^2xtanx

sorry haha


Can it not be tans^2x though? If not why not?
Original post by delta-T
Doing C4 trig, any idea how you would you integrate this? Thanks!


Set u=tanx and use integration by substitution. This comes up a lot in FP3 papers
Reply 12
Avatar for Notnek
Notnek
21
Original post by bartbarrow
Set u=tanx and use integration by substitution. This comes up a lot in FP3 papers

At FP3 level you should really be doing a question like this by recognition.

C4 students should too but some aren't taught it well so have to resort to substitution.
Original post by notnek
At FP3 level you should really be doing a question like this by recognition.

C4 students should too but some aren't taught it well so have to resort to substitution.

Yes, I sat my FP3 paper about a month ago and you start to recognise them so you can do it by inspection, but if you aren't at that point yet one of the best ways to prove it is to use a substitution.
Reply 14
Avatar for delta-T
delta-T
OP
5
Original post by alevelstresss
crap yeah sorry my heads messed up

its because with sec^2x you differentiate as 2secx times the derivative of sec x which is sec x tan x

so d(sec^2x)/dx is 2secxsecxtanx or 2sec^2xtanx

sorry haha


Ok I get that, but how would you know that if you didn't know he answer was sec^2x?
That's what I don't get
Reply 15
Avatar for Ventsi21
Ventsi21
Original post by Rafoleeno
Can it not be tans^2x though? If not why not?


It can be tan^2 x. Differentiating it: Bring the two down then differential of tan= sec^2 x therefore it will be 2tanxsec^2x
Original post by Ventsi21
It can be tan^2 x. Differentiating it: Bring the two down then differential of tan= sec^2 x therefore it will be 2tanxsec^2x


But why is the answer sec^2x even though it's tan^2x=sec^2x
Reply 17
Avatar for Ventsi21
Ventsi21
Original post by Rafoleeno
But why is the answer sec^2x even though it's tan^2x=sec^2x


No idea
Original post by Ventsi21
No idea


Original post by Rafoleeno
But why is the answer sec^2x even though it's tan^2x=sec^2x


I've been wondering this myself, and think that it could be that you take '1' from the c term in tan^2x + c to give tan^2x + 1 + b (some other constant) which gives sec^2x + b and for whatever reason, this is more useful but... :dontknow: :iiam:
Reply 19
Avatar for Notnek
Notnek
21
Original post by delta-T
image.jpeg
Apparently it's sec^2x??

Either sec^2(x) or tan^2(x) would be correct here, as SeanFM has explained.

Constants of integration are not needed when using integration by parts so either is fine.

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you