Integration advice needed (1 Viewer)

leehuan

Well-Known Member
Joined
May 31, 2014
Messages
5,805
Gender
Male
HSC
2015
How would you tackle integrals of the form



where m is odd and n is even?


(Within the scope of MX2)
 

Paradoxica

-insert title here-
Joined
Jun 19, 2014
Messages
2,556
Location
Outside reality
Gender
Male
HSC
2016
Use integration by parts to construct a two-step recurrence relation in both variables.

Alternatively, convert it into the fundamental trigonometric ratios and reduce the cosines and sines.
 

leehuan

Well-Known Member
Joined
May 31, 2014
Messages
5,805
Gender
Male
HSC
2015
Use integration by parts to construct a two-step recurrence relation in both variables.

Alternatively, convert it into the fundamental trigonometric ratios and reduce the cosines and sines.
Oh dear. So there isn't a trivial substitution like the two other cases have?
 

InteGrand

Well-Known Member
Joined
Dec 11, 2014
Messages
6,109
Gender
Male
HSC
N/A
I'm afraid this case is the most tedious of the bunch.
 

photastic

Well-Known Member
Joined
Feb 11, 2013
Messages
1,848
Gender
Male
HSC
2014


What they mean by equations 1 is the circle identity of secx and tanx, and the derivative of tanx and secx.
 

leehuan

Well-Known Member
Joined
May 31, 2014
Messages
5,805
Gender
Male
HSC
2015
Oh sorry lol, I was thinking of a sec rather than sec^2 being the thing expanded.

Ouch. Figures, my suspicions were right. (Might need a tiny revision in those notes @ photastic)

Thank goodness we have reduction formulae I guess...
 

InteGrand

Well-Known Member
Joined
Dec 11, 2014
Messages
6,109
Gender
Male
HSC
N/A
Ouch. Figures, my suspicions were right. (Might need a tiny revision in those notes @ photastic)

Thank goodness we have reduction formulae I guess...
Yeah, you may want to pre-derive that formula before setting out to tackle an integral like this so that you have it handy if you need it.
 

Paradoxica

-insert title here-
Joined
Jun 19, 2014
Messages
2,556
Location
Outside reality
Gender
Male
HSC
2016
As an aside, what about the ever so disgusting tangent half angle substitution?

Is that a viable method?
 

InteGrand

Well-Known Member
Joined
Dec 11, 2014
Messages
6,109
Gender
Male
HSC
N/A
It's probably horrifyingly tedious most of the time. But in principle it'd work.
 

photastic

Well-Known Member
Joined
Feb 11, 2013
Messages
1,848
Gender
Male
HSC
2014
Ouch. Figures, my suspicions were right. (Might need a tiny revision in those notes @ photastic)

Thank goodness we have reduction formulae I guess...
Lol they're from MATH1251 :p
 

braintic

Well-Known Member
Joined
Jan 20, 2011
Messages
2,137
Gender
Undisclosed
HSC
N/A
How would you tackle integrals of the form



where m is odd and n is even?


(Within the scope of MX2)
Actually the Ext 2 syllabus specifically states that these questions are NOT part of the course:

"Recurrence relations such as ....... which involve more than one integer parameter, are excluded."
 

InteGrand

Well-Known Member
Joined
Dec 11, 2014
Messages
6,109
Gender
Male
HSC
N/A
Actually the Ext 2 syllabus specifically states that these questions are NOT part of the course:

"Recurrence relations such as ....... which involve more than one integer parameter, are excluded."
Maybe leehuan meant when the m and n are particular numerical values rather than parameters? E.g. finding something like ∫sec3 x tan2 x dx.
 

Paradoxica

-insert title here-
Joined
Jun 19, 2014
Messages
2,556
Location
Outside reality
Gender
Male
HSC
2016
Actually the Ext 2 syllabus specifically states that these questions are NOT part of the course:

"Recurrence relations such as ....... which involve more than one integer parameter, are excluded."
I see no reason as to why double parameter integrals should not be part of the HSC.
 

braintic

Well-Known Member
Joined
Jan 20, 2011
Messages
2,137
Gender
Undisclosed
HSC
N/A
Maybe leehuan meant when the m and n are particular numerical values rather than parameters? E.g. finding something like ∫sec3 x tan2 x dx.
Actually he probably did. I didn't read the post properly and missed "of the form".
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top