recurrence formula (1 Viewer)

tutor01

Member
Given I_n = integral of x^n divided by sqrt(x^2-a^2) dx show that

nI_n - (n-1)a^2I_(n-2)=x^(n-1)sqrt(x^2-a^2).

I can't prove it. Can anyone help. Note I_n means I then subscript n like for recurrence integral questions.

Thanks!

Last edited:

tutor01

Member
Brilliant. I got to line 4 but did not then multiply by the root x^2-a^2 on itself. Thanks a lot.

Mechanic

New Member
the 2nd last line the subscript for a^2(n-1) is n-2 but in your last line it is n-1,

your therefore line is incorrect...

Carrotsticks

Retired
the 2nd last line the subscript for a^2(n-1) is n-2 but in your last line it is n-1,

your therefore line is incorrect...
Clearly just a typo.

nightweaver066

Well-Known Member
the 2nd last line the subscript for a^2(n-1) is n-2 but in your last line it is n-1,

your therefore line is incorrect...
I'll edit it if it's bothering you that much.

asianese

Σ
You can also do this question by splitting and then doing the +a^2-a^2 trick inside the x^2 bracket.