A blacksmith has been studying vector calculus and wants to calculate the total mass of a curved metal fitting. Given that the m
etal fitting has a helix shape parameterized by C:[0,π] → IR3 C(t) = (cos (t), sin(t), t) And the density of the metal material is given by the function:f(x,y,z) = 22 How can the black smith calculate the total mass of the fitting and what is this mass?
1 answer:
Answer:
4483.1
Step-by-step explanation:
Helix shape of the metal fitting parameterized :
C(t) = (cos(t), sin(t), t )
This shows that: x = cos(t), y = sin(t), z = t
density of the metal can be represented as
f (x(t), y(t), z(t) = 2z = 2t
To calculate the mass of the fitting an integral is generated below ( attached below is remaining part of the solution )
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