Reduction formula question

[Jun555vo]

Can anyone help with this question I’ve been stuck on it for ages! Thanks

 

[firemath]

Where are you stuck? What have you come up with so far? We can't help you well unless we know!

See the forum guidelines here.

 

[Dr.Peterson]

What does [MATH]I_p[/MATH] mean? This requires context.

 

[Jun555vo]

Hi I’m struggling to get started on this question. I know how to do part ii) but I’m really not sure on part i). Any help would be much appreciated

 

[Dr.Peterson]

What topics have you learned recently that you might use?

I tend to expect something like this to use integration by parts (though it isn't immediately obvious how to use it here). Can you make a start and show your work? Even work that is definitely wrong can be useful in helping you.

 

[topsquark]

It's a little messy but can you write out [math]\dfrac{1}{ x^{2p} (x^2 - 1) }[/math] and [math]\dfrac{1}{ x^{2p + 1} (x^2 - 1) }[/math] in terms of partial fractions? The problem becomes relatively easy, so long as you take the time to get the algebra straight.

-Dan

 

[Steven G]

Hi,
Did you really think that we could have helped you without know the integral?

 

[Jun555vo]

What topics have you learned recently that you might use?

I tend to expect something like this to use integration by parts (though it isn't immediately obvious how to use it here). Can you make a start and show your work? Even work that is definitely wrong can be useful in helping you.

Ok I’ll give integration by parts a try thanks

 

[Jun555vo]

It's a little messy but can you write out [math]\dfrac{1}{ x^{2p} (x^2 - 1) }[/math] and [math]\dfrac{1}{ x^{2p + 1} (x^2 - 1) }[/math] in terms of partial fractions? The problem becomes relatively easy, so long as you take the time to get the algebra straight.

-Dan

Yeah I tried that but the algebra got kinda messy so I gave up but I’ll try it again. Also shouldn’t the power be x^(2p+2) rather than x^(2p+1)? I just want to make sure that I’ll be doing it right

 

[Jun555vo]

Hi,
Did you really think that we could have helped you without know the integral?

I accidentally cropped out the top part of the picture is all

 

[Steven G]

Hi I’m struggling to get started on this question. I know how to do part ii) but I’m really not sure on part i). Any help would be much appreciated View attachment 19102

Can you compute the integral for I⁰? Just solve the integral with p=0. Then try to compute the integral for I₁. See if you can find a and b_p. If you can't then do you do to compute I₃.