fairly new to integration...need help (1 Viewer)

[ToO LaZy ^*]

Ok...here's the situation...
we started 4u trig integration before we even started the 3u component...
so i am very confused about integration of 'trig functions'....our teacher kinda skipped this part coz he knew our 3u class hasn't done it and now i'm going back to it and i don't really have a clue...

so could someone help start me up and maybe give a short lesson or something..?
or maybe i'll just give you some questions..

(these are like the first few question in the text, so they may seem easy)

differentiate:
sec^3x
cot^5x
cosec^4x

integrate:
sec^3xtanx
cot^2x
cos^3xsin^2x
cos^5xsin^4x

ok...here are some starters which i don't quite get...
help would be greatly appreciated
thx in advance..

 

[George W. Bush]

uh, you know how to differentiate, don't you.

if so, do so. awareness will soon dawn.

 

[ToO LaZy ^*]

yes i do, but there are some integtration i plainly don't get, maybe because i wasn't taught it

 

[George W. Bush]

well, for example.

differentiate sec^3x.
We know this is 3sec^3x tanx

now, looking at what you have to integrate
sec^3 tanx appears! Now, we know that d(sec^3x) = 3sec^3x tanx, so the integral of sec^3x tanx is 1/3 sec^3 x + c
the same applies for the others

for questions where you're not given d f(x)/dx = something you need to look at the integral. now d(secx)/dx = secxtanx, using a u substitution you have u^2, which is 1/3 u^3 + c as above (change variable back)

 

[ToO LaZy ^*]

Originally posted by George W. Bush
well, for example.

differentiate sec^3x.
We know this is 3sec^3x tanx

.....er...we do?....
is there some kind of rule that i should know about?

 

[Teoh]

Heh heh, yay another person who is so oblivoius to 4u!!!

I think the rule you're looking for is the basic chain rule one...

d/dx f(x)ⁿ = nf(x)^n-1 x f'(x)


I think???

 

[George W. Bush]

to do it in terms
f(x) = sec^3 x
Let u = secx
du/dx = secxtanx
f(x) = u^3
d f(x)/ du = 3u^2

therefore f'(x) = 3u^2 x secxtanx
= 3sec^2x x secxtanx
= 3 sec^3x tanx

 

[ToO LaZy ^*]

ah...icic..
thx georgie..

 

[ToO LaZy ^*]

any other examples anyone can help me with?...

 

[Grey Council]

for the differentiate questions, you just need the laws.

try getting a textbook with the differentials.
hehe

 

[ToO LaZy ^*]

aight...
i just realised that the Terry Lee book doesn't have any of those standard trig integration or differentiation..arghh!

 

[Teoh]

Yeah...you would be wanting to look at the
Cambridge 3 unit book, and the Preliminary course as well...

They have it all...

 

[ToO LaZy ^*]

are fitzpatrick any good?
i've got 3/4U texts but havn't really gone through it yet..

 

[Grey Council]

hell yes.

Fitzpatrick is darn good.
cept the 4u section on complex numbers.
:-\

but yeah, use it. I take no responsibility for the 4u one, but the 3u one i can testify is quite good.

 

[ToO LaZy ^*]

excellent....

 

[:: ck ::]

3u one is sooo hard ><"
hardest 3u textbook in my opinion...