Integration by Parts Homework: Get Help Now

[uzman1243]

Homework Statement

Homework Equations

N/A

The Attempt at a Solution

I can't even begin the attempt because I don't know how you could use intergration by parts for this sum in the first place.
Can you help me out?

 

[SteamKing]

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.

 

[SammyS]

Homework Statement

Homework Equations

N/A

The Attempt at a Solution

I can't even begin the attempt because I don't know how you could use intergration by parts for this sum in the first place.
Can you help me out?

What sum ?

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

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

 

[lurflurf]

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

 

[mafagafo]

This does not look like precalculus.

 

[uzman1243]

What sum ?

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

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

Lol. He did.

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

 

[SammyS]

Lol. He did.

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

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


Try it and see what happens !