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streetyfatb
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#1
Report Thread starter 14 years ago
#1
Hi, ive been doing exams & what not, so ive missed this chapter and im working through it. Im stuck on a particular question & would like to be shown how you go about solving the question:

Pi/2
∫cot^n[θ] dθ
Pi/4

Using the Induction Formulae find:

I7

I8

Many Thanks

Streety
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elpaw
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#2
Report 14 years ago
#2
to find I_n, you integrate by parts

Pi/2
∫cot^(n-2)[θ] cot^2[θ] dθ
Pi/4

this will give you I_n in terms of I_(n-2)

hence to find I_8, you use it to get it in terms of I_6, which you can get in terms of I_4, which you can get in terms of I_2, which is trivially integrable

the same goes for I_7, but you will get it in terms of I_1, which is the integral of cot[θ] = cos[θ]/sin[θ] which again is trivially integrable (you get a log)
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streetyfatb
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#3
Report Thread starter 14 years ago
#3
I understand the idea behind this but how do i go about integrating

Pi/2
∫cot^(n-2)[θ] cot^2[θ] dθ
Pi/4

And getting this in the required form?

Many Thanks

Streety
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Womble548
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#4
Report 14 years ago
#4
cot^2x + 1 = cosec^2x

use that!
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