Urgent: when splitting up to make a recurrence relation how do we split the n up (1 Viewer)

[Stressedaf0666]

take this as an example, how would we know that we have to split it up so that it is sin n-1 sinetc.

wut tells us that

 

[mmmmmmmmaaaaaaa]

Usually what you're trying to show that integral equals to will give you some guidance as to how you should split it up

 

[SCREW L+S]

Usually what you're trying to show that integral equals to will give you some guidance as to how you should split it up

aah so if the thing includes n-1 is it recommended to split it up like that or smthg

 

[yanujw]

I looked up the question in cambridge and it appears that it asks you for a relationship between u(n) and u(n-2)
Think carefully about the cases before you write anything.

Case 1: Using the factors sin^n(x) and cos^2(x)
The integral of cos^2x is quite complicated in that involves sin(2x)/4, which isn't likely to give us a convenient recurrence relation. So it probably won't work

Case 2: Using the factors sin^(n-1)x and sinxcos^2(x)
The integral of sinxcos^2(x) is cos^3(x)/3 which is a bit more convient to work with. Also the derivative of sin^(n-1)x is (n-1)sin^(n-2)xcosx. The fact that you have a sin^(n-2)x term, and that you need to involve u(n-2), is a huge hint to use these factors.

 

[mmmmmmmmaaaaaaa]

aah so if the thing includes n-1 is it recommended to split it up like that or smthg

Yes