A thin wire of density pxyyx2 has the shape of a parabola yx

A thin wire of density p(x,y)=y-x+2 has the shape of a parabola, y=x^2 from (-2,4) to (0,0). Set-up an integral to find the mass of the wire.

Data.

(x,y)= y-x+2

y = x² (keep in mind for replacing)

boundaries are;

from (-2,4) to (0,0)

Answer.

Density mass integral is given by:

m = _c (x,y) ds

_-2⁰₀^x2 (y-x+2) dydx

_-2⁰ [y²/2 - xy + 2y]₀^x2 dx

_-2⁰ [x⁴/2 - x³ + 2x²]₀^x2 dx

[x⁵/10 - x⁴/4 + 2x³/3]₂⁰ dx

0 - [-32/10 - 4 - 16/3]

= 32/10 + 4 + 16/3

= 188/15