# Integration by parts

1. May 4, 2014

### uzman1243

1. The problem statement, all variables and given/known data

2. Relevant equations

N/A

3. The attempt at a solution

I cant even begin the attempt because I dont know how you could use intergration by parts for this sum in the first place.
Can you help me out?

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2. May 4, 2014

### SteamKing

Staff Emeritus
First of all, I(n) is not a sum. I is a function which depends on the exponent of the sine function in the integrand.

You might try to determine what I(n) is for some discrete values of n, like n = 2, 3, 4, etc. and see if a pattern emerges.

3. May 4, 2014

### SammyS

Staff Emeritus
What sum ?

Let u = sin(n-1)(x), and dv = sin(x) dx

(The King beat me by fractions of a minute!)

4. May 4, 2014

### lurflurf

hint
$$\int\! \sin^n(x) \, \mathrm{d}x=\int\! \sin^{n-2}(x)\sin^{2}(x) \, \mathrm{d}x=\int\! \sin^{n-2}(x)\big(1-\cos^{2}(x)\big) \, \mathrm{d}x$$

5. May 4, 2014

### mafagafo

This does not look like precalculus.

6. May 4, 2014

### uzman1243

Lol. He did.

Anyways, can you tell me why sin(n-1)(x)?

7. May 4, 2014

### SammyS

Staff Emeritus
(n-1) is half way from n to (n-2) .

Try it and see what happens !