what is the integral of (a^2 - x^2) ^(1/5).?

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what is the integral of (a^2 - x^2) ^(1/5).?

2006-09-09 21:34:57 · 3 answers · asked by henry K 1 in Science & Mathematics ➔ Mathematics

3 answers

You can't do this integral in elementary terms. If you integrate it from x=0 to x=a, it is related to the value ofa Bessell function.

2006-09-10 01:36:41 · answer #1 · answered by mathematician 7 · 2⤊ 0⤋

Denote the integral by I
Let x=a sint
dx=acost dt

Then
x^2=a^2. (sint)^2

a^2-x^2=a^2-a^2 (sint)^2=a^2 . (cost)^2

I = integral( a^(7/5). (cost)^(7/5).dt )

I = a^(7/5). integral( (cost)^(7/5).dt )
Try to calculate this last integration.

2006-09-10 04:56:21 · answer #2 · answered by iyiogrenci 6 · 0⤊ 1⤋

2006-09-10 05:08:09 · answer #3 · answered by kitty*love 3 · 0⤊ 1⤋