Mass of a wire

[Rosana]

A thin wire has the shape of the curve [MATH]x = sqrt(9-y^2)[/MATH] from 0 ≤ y ≤ 3. Calculate the mass of this wire, considering that its linear mass density is given by ρ(x, y) = [MATH]x*sqrt(y)[/MATH].

I parameterized the circumference going from 0 to pi. However, by calculating the line integral, I got a mass of 0. Is that correct?

 

[Deleted member 4993]

A thin wire has the shape of the curve [MATH]x = sqrt(9-y^2)[/MATH] from 0 ≤ y ≤ 3. Calculate the mass of this wire, considering that its linear mass density is given by ρ(x, y) = [MATH]x*sqrt(y)[/MATH].

I parameterized the circumference going from 0 to pi. However, by calculating the line integral, I got a mass of 0. Is that correct?

Absolutely, positively NOT!

Please share your work in detail - so that we can correct your mistake/s!

 

[Rosana]

 

[skeeter]

[MATH]0 \le y \le 3 \implies[/MATH] limits of integration should be [MATH]0[/MATH] to [MATH]\dfrac{\pi}{2}[/MATH]

 

[Rosana]

Oh, i was interpreting de positive and negative values from the square root. So dumb. Thanks!

 

[skeeter]

[math]\rho = x\sqrt{y} \ge 0 \implies y \ge 0[/math]
[math]x = \sqrt{9-y^2} \implies x \ge 0[/math], also