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Prove the following reduction formula: integrate of ((cosx)^n) dx =1/n(cos^(n-1)x)(sin(x)) + ((n-1)/n) integrate of cos^(n-2)dx

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mlehuzzah eNotes educator | Certified Educator

calendarEducator since 2012

write251 answers

starTop subjects are Math and Literature

Use integration by parts:

`u="cos" ^(n-1) x`                              `dv = "cos" x`

`du = (n-1)( "cos"^(n-2) x)( -"sin" x) dx`      `v="sin" x`

 

Then

`int "cos" ^n x dx = "cos"^(n-1)...

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