# Another simple question that I don't get

1. Mar 1, 2008

### r6mikey

[SOLVED] Another simple question that I don't get :(

1. The problem statement, all variables and given/known data
Find the Length of the indicated curve

y=2x-3 x[1-3]

2. Relevant equations

Arc Length=$$\int$$$$\sqrt{1+[f'(x)]^{2}dx}$$

3. The attempt at a solution

ok so y'=2 of course,

so it becomes a problem of $$\int from 1 to 3 for \sqrt{5}$$

using substitution, u=5 ,and this is where i get a little confused....

du=0dx which would make dx=du/0

the answer becomes 2$$\sqrt{5}$$

I'm sure I'm making it harder than it is, I always do..... :(

2. Mar 1, 2008

### r6mikey

and thinking about it, i should probably not be using the formula for arc length for this problem, even though it is in the arc length chapter...since this is a linear function

3. Mar 1, 2008

### r6mikey

using the arc length formula the only thing i can think of is that when i get

$$\sqrt{5}$$dx and dx ends up being 0, it becomes neglible so i only have $$\sqrt{5}$$ to evaluate from 1 to 3.... but then my question would be, I know subtracting 3$$\sqrt{5}$$ from 1$$\sqrt{5}$$ gives me the answer 2$$\sqrt{5}$$ but there is no X in front of the $$\sqrt{5}$$

:(

4. Mar 1, 2008

In the formula for arc length, the dx should be OUTSIDE of the radicand. Does this help you?

Hint: it should!

What is $$\int_1^3\sqrt{5}*dx$$

Last edited: Mar 1, 2008
5. Mar 1, 2008

### r6mikey

yea sorry, forgot to put the dx on the outside, but still confused.... using substitution and writing the problem like this.....

u$$^{1/2}$$ where u=5, du=0dx so dx=du/0 which is ?

continuing, if it is right u$$^{1/2}$$du would become u$$^{3/2}$$ times 2/3 so I'm doing something wrong with the substituion.....I'm just confusing meself :(

I can do all the problems except this one b/c when I take the derivative of u it becomes nothing..... so that is where im getting lost

Last edited: Mar 1, 2008
6. Mar 1, 2008

What are you doing? Why the need for u sub? Again I ask you what is $$\int c*dx$$

where c is any constant.....any constant like, oh let's say $\sqrt 5$

7. Mar 1, 2008

### r6mikey

so you're saying it would just become (integral)c=x so x(sqrt 5)

I'm not seeing the obvious, for some reason i 'm thinking i need substitution....wtf

Last edited: Mar 1, 2008
8. Mar 1, 2008

Of course! sqrt5 is just a number, just some constant. Pull it through the integral and proceed as normal. Evaluate what you have from x=3--->x=1

---->(3-1)*$\sqrt 5$

$$\int_{x_0}^x cdx=c\int_{x_o}^x dx=c[x]_{x_o}^x$$

What is there to substitute? What are you going to replace with u?

Last edited: Mar 1, 2008
9. Mar 1, 2008

you with me?

10. Mar 1, 2008

### r6mikey

I believe so, i just think i gotta step away from these books for awhile:yuck:

11. Mar 1, 2008