Intergration problem

[CraXshot]

must find the length of the arc of the curve on the given interval of x:

The Curve: 24xy=x⁴ +48 Interval : x=2 to x=4

 

My solution gives a math error and i've been over and over it and I can't find my fault. I'm known too make a lot of small errors so please help me find it.

you'll see at the end when I substitute 2 I get an undefined anwer(Divide by 0)

 

 

I have attached my solution. Please help if you can

 

 

I

Edited August 23, 2011 by CraXshot

[Schrödinger's hat]

must find the length of the arc of the curve on the given interval of x:

The Curve: 24xy=x⁴ +48 Interval : x=2 to x=4

 

My solution gives a math error and i've been over and over it and I can't find my fault. I'm known too make a lot of small errors so please help me find it.

you'll see at the end when I substitute 2 I get an undefined anwer(Divide by 0)

 

 

I have attached my solution. Please help if you can

 

 

I

 

Check your integral? Show us the rest of the working there or explain the process by which you got from the second to last to the last line. I think that may be at fault (I can't see anything else wrong).

[CraXshot]

Check your integral? Show us the rest of the working there or explain the process by which you got from the second to last to the last line. I think that may be at fault (I can't see anything else wrong).

 

I intergrated it, if you deffirentiate the answer using the chain rule(working from the anwer upwards ) :

 

Dx (2/3)[(1/2)+(x⁴/64)+(4/x⁴)]^3/2

(x³/16 - 16/x⁵)

 

 

= (1/2 + x⁴/64 + 4/x⁴)^1/2

 

I find the term i wish to intergrate

So according to me it must be right, but there must be a fault

[Schrödinger's hat]

Not quite following your reasoning.

If you were to expand that w/ product rule the function in the integral would be one term, the other would be

[math]\left(\frac{2}{3}\left(\frac{1}{2}+\frac{x^4}{64}+\frac{4}{x^4}\right)^\frac{3}{2}\right)\frac{d}{dx} \left(\frac{1}{\frac{x^3}{16} - \frac{16}{x^5}}\right)[/math]

Edited August 24, 2011 by Schrödinger's hat

[CraXshot]

Ok can you just please explain to me whythat one factor that needs to be differtiated( or if I can ask it simple: why does it have the d/dx in front of it)...

 

 

 

 

 

 

I noticed that if I worked back from my answer using the Qoutient rule it didn't work out after the minus so I couldn't find the intergral . I am missing something with the intergration step.

If you or someone can please just look at the question in the begginning and work it out to show me how you intergrated it. The anwer is 11/6 but I still dont get that even when using:

 

 

 

 

 

 

 

[Schrödinger's hat]

That was the other term that should show up when you use the quotient rule from your answer.

Don't have time right this second to work it from the beginning, but it looks like the type of thing a trig substitution would work on.

 

Another option would be to try a different variable. Rearrange for y, or find some other parameter that takes you along the curve.

[CraXshot]

Ok I tried what I could think of but still noting,I can't get the intergration right

[Schrödinger's hat]

I don't get 11/6 unless I've dropped a minus sign (which happens frequently enough).

But the method is easy enough. It's a bit easier to see if you take 1/x^2 out of the brackets.

[math] \frac{1}{x^2}\sqrt{ \frac{x^4}{2}+\frac{x^8}{64} + 4}[/math]

 

[math] \frac{1}{x^2}\sqrt{ (\frac{1}{8}x^4 + 2)^2}[/math]

Remove the square root and you're away

Edited August 25, 2011 by Schrödinger's hat

[CraXshot]

Ok thanks alot for the help , I just couldn't see it. I also don't get 11/6 but i'll confirm the correct answer after class.