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Question: Find the length of the curve 24xy = x^4 + 48 between (2, 4/3) and (3, 43/24). Answer is supposed to be 9/8.

This is the formula (I think): square root(1 + (dy/dx)^2 dx)

I tried to integrate and I did it like this:

dy/dx = 3/24 x^2 - 2x^-2 or 3/24 x^2 - 2/x^2

then: square root(1 + (3/24 x^2 -2x^-2)^2)

= square root(1 + (1/64 x^4 - 4x^-4))

now integration:

(1 + (1/64 x^4 - 4x^-4))^(1/2)

= (2/3) (1 + (1/64 x^4 - 4x^-4))^(3/2) (x + (1/320 x^5 + 4/3 x^-3)

That's how far I got, I think it's wrong. If anyone could help me out, I would appreciate it. Thanks.

This is the formula (I think): square root(1 + (dy/dx)^2 dx)

I tried to integrate and I did it like this:

dy/dx = 3/24 x^2 - 2x^-2 or 3/24 x^2 - 2/x^2

then: square root(1 + (3/24 x^2 -2x^-2)^2)

= square root(1 + (1/64 x^4 - 4x^-4))

now integration:

(1 + (1/64 x^4 - 4x^-4))^(1/2)

= (2/3) (1 + (1/64 x^4 - 4x^-4))^(3/2) (x + (1/320 x^5 + 4/3 x^-3)

That's how far I got, I think it's wrong. If anyone could help me out, I would appreciate it. Thanks.

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