# Center of Mass via Scalar Line Integrals

## Homework Statement

A thin wire has the shape of the first quadrant part of the circle with center at the origin and radius a. If the density function is rho(x,y)=kxy, find the mass and center of mass of the wire.

## Homework Equations

My parametric equation of the circle was x=a*cos(t) and y=a*sin(t).

## The Attempt at a Solution

I really have no clue where to begin for finding the center of mass of the wire. I think I got the mass via integral(k*a^2*sin(t)*cos(t) dt = -(k*a^2)/2. Thanks for the help!

## Answers and Replies

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tiny-tim
Science Advisor
Homework Helper
Hi Hashmeer!

(try using the X2 tag just above the Reply box )
… I think I got the mass via integral(k*a^2*sin(t)*cos(t) dt = -(k*a^2)/2.
No, mass = ∫ density*d(length),

and d(length) is not dt, it's … ?

Yea, I looked over my notes and I figured out what I need to do. Thanks for confirming what I was thinking was wrong.