This integral must be simple enough for you
As for number 2
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