[sucess]

Click on the picture to see the question

[ttoby]

Do you have to integrate this? See if you can spot a trigonometric term and its derivative in there to guess which substitution to use.

[P.h.o.e.n.i.x.y]

I think you can integrate directly. integration of sec^2xtanx. Integral of sec^2x is tan x

[P.h.o.e.n.i.x.y]

and integral of tan x is -ln (cos x) --> just change tan x into sin x/cos x.

then use the formula of product integration.

[sucess]

thank you i will try

[elldeegee]

(Original post by 3uNic3)
and integral of tan x is -ln (cos x) --> just change tan x into sin x/cos x.

then use the formula of product integration.

I don't remember being required to know this at A-level. In fact, i dont even know it now, i have to look it up (but maybe that's my own shortcoming and if it is, i apologise, i dont mean to cause offence either way)

(Original post by sucess)
Click on the picture to see the question

Basing it on what i remember from A-level i would expect that you should use integration by substitution.
where now work out and rearrange so you get as the subject.

substitute everything into your original question, and you should get out what you want.


HINT: [i would put this as a spoiler, but i dont know how]
don't do anything with the originally! Leave it as it is, you should see why...

[P.h.o.e.n.i.x.y]

(Original post by elldeegee)
I don't remember being required to know this at A-level. In fact, i dont even know it now, i have to look it up (but maybe that's my own shortcoming and if it is, i apologise, i dont mean to cause offence either way)




Basing it on what i remember from A-level i would expect that you should use integration by substitution.
where now work out and rearrange so you get as the subject.

substitute everything into your original question, and you should get out what you want.


HINT: [i would put this as a spoiler, but i dont know how]
don't do anything with the originally! Leave it as it is, you should see why...

It's probably because the exam board our school used were different. My school used OCR. For C4, I had to know both methods (the one I said and the substitution) and I can choose whichever method I want unless stated otherwise. Well, at least I was thought both methods, so I'm not sure about yours.

[TheJ0ker]

(Original post by elldeegee)
I don't remember being required to know this at A-level. In fact, i dont even know it now, i have to look it up (but maybe that's my own shortcoming and if it is, i apologise, i dont mean to cause offence either way)

It is in the A-level formula book, very occasionally it is required though.

(Original post by elldeegee)
Basing it on what i remember from A-level i would expect that you should use integration by substitution.
where now work out and rearrange so you get as the subject.

substitute everything into your original question, and you should get out what you want.


HINT: [i would put this as a spoiler, but i dont know how]
don't do anything with the originally! Leave it as it is, you should see why...

^^ This is probably the most effective way to integrate it. I am pretty sure you could use integration by parts as well if you so desired.

[elldeegee]

(Original post by 3uNic3)
It's probably because the exam board our school used were different. My school used OCR. For C4, I had to know both methods (the one I said and the substitution) and I can choose whichever method I want unless stated otherwise. Well, at least I was thought both methods, so I'm not sure about yours.

Ah i suppose.
OP, you may want to try the method of substitution, because if the question specifically asks for it (and sometimes it does) then, provided it is correct, the only mark you will get (out of a potentially 3+ mark question) is the answer mark.

(my method does work as i did it and also checked my answers on wolfram)

[P.h.o.e.n.i.x.y]

(Original post by elldeegee)
Ah i suppose.
OP, you may want to try the method of substitution, because if the question specifically asks for it (and sometimes it does) then, provided it is correct, the only mark you will get (out of a potentially 3+ mark question) is the answer mark.

(my method does work as i did it and also checked my answers on wolfram)

Yeah, both works the same way. But in more complicated questions, like involving ln, integration by parts is more commonly used. So, I kind of get used to it and use that all the time, coz I'm familiar with it, so I can use it pretty quickly.

but either way is fine as long as the answer is right

[elldeegee]

(Original post by 3uNic3)
Yeah, both works the same way. But in more complicated questions, like involving ln, integration by parts is more commonly used. So, I kind of get used to it and use that all the time, coz I'm familiar with it, so I can use it pretty quickly.

but either way is fine as long as the answer is right

i agree, as soon as i see ln i use by parts.

and i tried using by parts on the q provided by the OP, but as i had never known to remember what you suggested, i didnt think of that automatically, instead i converted sec^2 to 1+tan^2 and then it iinvolved integrating tan^3 which i didnt like the look of... so stopped

[P.h.o.e.n.i.x.y]

(Original post by elldeegee)
i agree, as soon as i see ln i use by parts.

and i tried using by parts on the q provided by the OP, but as i had never known to remember what you suggested, i didnt think of that automatically, instead i converted sec^2 to 1+tan^2 and then it iinvolved integrating tan^3 which i didnt like the look of... so stopped

I don't think you can really integrate tan^3 directly. lol. you can never integrate trigo with powers directly, just like sin^2, have to change it to something like 1/2 - 1/2cos 2x. i think the integral of tan x is in the formula booklet --> ln (sec x ) or -ln (cos x). Or you can work it out. it's easy. you convert tan x into sin x/cos x. And differential of cos x is - sin x. just use one of the concept in integration and you'll get it.