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 integration

Can anyone explain how to integrate sec^2(x)tanx ? thanks
Original post by coconut64
Can anyone explain how to integrate sec^2(x)tanx ? thanks


Note that the derivative of tanx is sec^2x, so you can apply the reverse chain rule


Posted from TSR Mobile
Original post by coconut64
Can anyone explain how to integrate sec^2(x)tanx ? thanks


Think about what differentiates to give something that looks similar. :h:
You could recognize that sec^2x is the derivative of tan x or use a u substitution, let u = tanx

Original post by coconut64
Can anyone explain how to integrate sec^2(x)tanx ? thanks
Reply 4
Avatar for coconut64
coconut64
OP
16
Original post by NotNotBatman
You could recognize that sec^2x is the derivative of tan x or use a u substitution, let u = tanx


I get how to obtain the sec^2x part but what about the tanx part? Also what about secx as this gives me secxtanx...

Thanks
Reply 5
Avatar for coconut64
coconut64
OP
16
Original post by SeanFM
Think about what differentiates to give something that looks similar. :h:


I know that secx gives secxtanx but this doesn't give me sec^2 x though...

Thanks
Original post by coconut64
I get how to obtain the sec^2x part but what about the tanx part? Also what about secx as this gives me secxtanx...

Thanks


ddx(tan(x))=sec2(x)\frac{d}{dx}(tan(x)) =sec^2(x), so what does differentiating tan^2x result in?
(edited 7 years ago)
Original post by coconut64
I know that secx gives secxtanx but this doesn't give me sec^2 x though...

Thanks


it's been given above, but it was tanx that you should be particularly interested in. It's worth looking at a list of all of those ones (sec, tan cosex, cot.. and what they differentiate to if you're stuck)
Original post by coconut64
I know that secx gives secxtanx but this doesn't give me sec^2 x though...

Thanks


Original post by SeanFM
it's been given above, but it was tanx that you should be particularly interested in. It's worth looking at a list of all of those ones (sec, tan cosex, cot.. and what they differentiate to if you're stuck)


Using the fact that differentiating sec x gives sec x tan x is an alternative to using the derivative of tan x.

I've always liked integrals that give you more than one answer and they look completely different at first sight (like sin x cos x)

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you