1. Find the mass of the wire.

Density at (x,y) is x; the wire occupies the portion of the parabola
y = (x^2)/2 from (0,0) to (1, 1/2)

2. A wire occupies the spiral r = e^@ corresponding to @ in [0,2pi]. the density of the wire at point (r,@) is r. Find the mass of the wire.

@ is theta btw; i don't know how to type out the symbol

thanks

2. $x= t$
$y= t^2$
$rho = t$
$|f'(t)| = \sqrt{1 + 4t^2}$
$m = \int rho \cdot |f'(t)| dt$
This integral must be simple enough for you
As for number 2
$x =t$
$r = e^t$
$rho = r = e^t$
$|f'(t)| = \sqrt{1+e^{2t}}$
$m = \int rho \cdot |f'(t)| dt$

3. much appreciated