aaaa REDUCTION .. grrrr (1 Viewer)

[3.1415926535897]

ok here is our lil reduction one


In = Int. (pi/4 to pi/2) Cot^n(x) dx.

Show = 1/(n - 1) - I(n-2)


Thanks mateys !!!!

 

[lucifel]

hmm this is a textbook reduction formula question:

I_n = ∫cotⁿ.dx (from pi/4 - pi/2)

=∫cot²xcot^n-2x.dx

=∫(cosec²x - 1)(cot^n-2x)dx

=∫cosec²xcot^n-2xdx - I_n-2 (by expansion)

=[-(cot^n-1x)/n-1]^pi/2_pi/4 - I_n-2

the thing in the bracket should equal 1/n-1
thus:

I_n = 1/(n-1) - I_n-2