# Homework Help: Length of Curve

1. Feb 8, 2010

### Precursor

1. The problem statement, all variables and given/known data
Find the length of the curve. $$y = x^{3/2}$$ from x = 0 to x = 4.

2. Relevant equations
$$L = \int^{b}_{a} \sqrt{1 + (dy/dx)^{2}} dx$$

3. The attempt at a solution
$$L = \int^{b}_{a} \sqrt{1 + (dy/dx)^{2}} dx$$
$$L = \int^{4}_{0} \sqrt{1 + (3x^{1/2}/2)^{2}} dx$$
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I used substitution rule
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$$L = 64/27$$

Is this correct?

Thanks

2. Feb 8, 2010

### Ratio Test =)

http://www.wolframalpha.com/input/?i=integrate+sqrt[+1+++[+(3/2)+x^(1/2)+]^2+]+from+x=0+to+x=4
Its better to post all of your work.

3. Feb 8, 2010

4. Feb 8, 2010

### Ratio Test =)

Yeah Its wrong.

You will face: $$\int_0^4 \sqrt{ 1 + \frac{9}{4}x } \;\ dx$$
What did you do for it?

5. Feb 8, 2010

### CompuChip

Actually I found $c(7 \sqrt{7} - 1)$,
where c is a numerical factor (I got 2/3) which I'm not sure of because I did the calculation sloppily.
So I suggest you show the rest of the calculation as well.

 Too slow, you already have several replies. [/edit]

6. Feb 8, 2010

### Precursor

That's exactly what I got, but when I used the substitution rule, to integrate, I did not change the limits of integration to in terms of u.

7. Feb 8, 2010

### Ratio Test =)

Ohhh.
BTW, Its a famous mistake. :)