Finding mass of circular piece of wire?

[Chandasouk]

Calculate the total mass of a circular piece of wire of radius 4cm centered at the origin whose mass density is\rho(x,y) = X² g/cm

I get that you have to parametrize the circular peace, giving you C(t) =(4cost, 4sint) but how do you get the bounds for t?

The solution states that it is -\pi<=t<=\pi but how?

Also, it's actually been a while since my class spoke on line integrals and I realized now that I have great difficulty parameterizing shapes and curves that gives me problems further on in Calc 3. Are there parametrization I should automatically know? For example how does a wire in the shape of a parabola y = x² parameterize to C(t) = (t, t^2) ?

 

[lanedance]

Calculate the total mass of a circular piece of wire of radius 4cm centered at the origin whose mass density is\rho(x,y) = X² g/cm

I get that you have to parametrize the circular peace, giving you C(t) =(4cost, 4sint) but how do you get the bounds for t?

The solution states that it is -\pi<=t<=\pi but how?

those represent a full revolution of a circle

Also, it's actually been a while since my class spoke on line integrals and I realized now that I have great difficulty parameterizing shapes and curves that gives me problems further on in Calc 3. Are there parametrization I should automatically know? For example how does a wire in the shape of a parabola y = x² parameterize to C(t) = (t, t^2) ?

Homework Statement

the cartesian equation of a circle is x^2 + y^2 = 1, that of a parabola is y = x^2

try substituting in the parametrix equations for x and y in each and you will see they are satisfied.

Note there is no unique paramterisation for these problems, just finding one that works (and is easy to use in the problem) is enough