How Do You Calculate the Length of a Line Segment in Calculus?

[r6mikey]

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

Homework Statement

Find the Length of the indicated curve

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

Homework Equations

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

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... :(

 

[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

 

[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}


:(

 

[Saladsamurai]

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

 

[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 I am getting lost

 

[Saladsamurai]

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

 

[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

 

[Saladsamurai]

\intc=x so you're saying it would just become x\sqrt{5}

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?

 

[Saladsamurai]

you with me?

 

[r6mikey]

I believe so, i just think i got to step away from these books for awhile

 

[Saladsamurai]

We all do! I feel the same way most of the time!