(Calc 3) Finding mass of a wire using line integral

[NWeid1]

Homework Statement

Find the mass of a wire in the shape of the parabola y=x² for $1 \leq x\leq2$ and with density p(x,y)=x.

Homework Equations

The Attempt at a Solution

I just want to make sure I am setting this integral up right. Here is what I did:

I parameterized the equation to x=t, y=t²
and then got $\int xds$ from 1 to 2.
then I set ds = $\sqrt{1+4t^2}*dt$

so I would have

$\int t*\sqrt{1+4t^2}dt$ from 1 to 2. Correct, or no?

 

[LCKurtz]

Homework Statement

Find the mass of a wire in the shape of the parabola y=x² for $1 \leq x\leq2$ and with density p(x,y)=x.

Homework Equations

The Attempt at a Solution

I just want to make sure I am setting this integral up right. Here is what I did:

I parameterized the equation to x=t, y=t²
and then got $\int xds$ from 1 to 2.
then I set ds = $\sqrt{1+4t^2}*dt$

so I would have

$\int t*\sqrt{1+4t^2}dt$ from 1 to 2. Correct, or no?

Yes.