Calculus Problem - 3D Arc Length: r(t)=<cos(4t) , -4t , sin(4t)> starting from r(-4)

[wpurvin97]

Calculus Problem - 3D Arc Length: r(t)=<cos(4t) , -4t , sin(4t)> starting from r(-4)

Find the arc length function for curve:
r(t)=<cos(4t) , -4t , sin(4t)> starting from r(-4).

1) Find s(t)
-Where s(t) = The integral from -4 to t of the magnitude of r'(t)

2)Use your arc length function to quick evaluate the length of r from
t=-4 to t=0
t=-4 to t=4

Thanks in advance,

-A struggling calculus student

 

[Deleted member 4993]

Find the arc length function for curve:
r(t)=<cos(4t) , -4t , sin(4t)> starting from r(-4).

1) Find s(t)
-Where s(t) = The integral from -4 to t of the magnitude of r'(t)

2)Use your arc length function to quick evaluate the length of r from
t=-4 to t=0
t=-4 to t=4

Thanks in advance,

-A struggling calculus student

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