Seven less than one half of x
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The mass of the wire is found to be 40π√2 units.
<h3>How to find the mass?</h3>To calculate the mass of the wire which runs along the curve r ( t ) with the density function δ=5.
The general formula is,
Mass =
To find, we must differentiate this same given curve r ( t ) with respect to t to estimate |r'(t)|.
The given integration limits in this case are a = 0, b = 2π.
Now, as per the question;
The equation of the curve is given as;
r(t) = (4cost)i + (4sint)j + 4tk
Now, differentiate this same given curve r ( t ) with respect to t.
Further simplifying;
Now, use integration to find the mass of the wire;
Therefore, the mass of the wire is estimated as 40π√2 units.
To know more about density function, here
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The complete question is-
Find the mass of the wire that lies along the curve r and has density δ.
r(t) = (4cost)i + (4sint)j + 4tk, 0≤t≤2π; δ=5
because y^3 is raised to the power of two, we will have to multiply the exponents rather than adding them.
By distributing the power of 2, we will get y^2(6).
Because now the exponents are being multiplied, we can just add them to get y^8. The other y has a power of 1, so we'll just add the power of that y as well to get y^9.
summary:
multiply exponents if they are being raised to a power.
add exponents if they are being multiplied, and only add them if they have the same base (in this case, both the bases of the exponents are y, so we can add them)
