I need help with this question

Use integration by parts to express:

I(n) = (int) sin^n(x) dx

in terms of I(n - 2). Hence show that:

(int) between pi/4 & pi/2 1/ sin^4(x) dx =4 / 3

help would be much appreciated

cheers.

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- August 30th 2006, 06:19 AMsterpsneed help with this integration by parts
I need help with this question

Use integration by parts to express:

I(n) = (int) sin^n(x) dx

in terms of I(n - 2). Hence show that:

(int) between pi/4 & pi/2 1/ sin^4(x) dx =4 / 3

help would be much appreciated

cheers. - August 30th 2006, 07:03 AMRandom333
Ok, I think I've worked out your explanation.

Integral in terms of x using n is

And on you go, hopefully....if I can work LaTeX - August 30th 2006, 07:54 AMGlaysherQuote:

Originally Posted by**sterps**

and

and

See if you can do the rest - August 30th 2006, 08:15 AMGlaysherQuote:

Originally Posted by**Random333**

- August 30th 2006, 08:20 AMSoroban
Hello, sterps!

This is a Reduction Formula derivation.

It's quite long and elaborate . . . better sit down.

Quote:

Use integration by parts to express:

in terms of

Given: .

Let:

Then:

We have: .

. . . . . . . .

. . . . . . . .

. . . . . . . .

. . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . This is

We have: .

. . . . . . . .

Therefore: .

*Whew!*. . . I need a nap . . .

- August 30th 2006, 02:24 PMsterps
thanks for the help guys.

ive never heard of Reduction Formula derivation. :confused: - August 31st 2006, 12:47 AMGlaysher
Well it is the name of what you are trying to do.

Kind of turning an integration problem into an iterative problem