- #1
Chandasouk
- 165
- 0
Calculate the total mass of a circular piece of wire of radius 4cm centered at the origin whose mass density is[tex]\rho[/tex](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 -[tex]\pi[/tex]<=t<=[tex]\pi[/tex] 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) ?
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 -[tex]\pi[/tex]<=t<=[tex]\pi[/tex] 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) ?