The arclength of the curve r(t) = 2 cos3 (πt/2), 2 sin3 (πt/2), 1, between the...

The arclength of the curve r(t) = 2 cos³ (πt/2), 2 sin³ (πt/2), 1, between the points r = (2, 0, 1) and r = (0, 2, 1), is given by?

Expert Solution

In the given problem we're given a space curve r(t)= 2 cos3 (πt/2) i + 2 sin3 (πt/2) j + 1 k

We need to find the arclength b/w points r=(2,0,1) and r=(0,2,1)

We know that the arclength is given by-

, where is the magnitude of the derivative of the given curve, which is integrated over given intervals a to b.

Here r=(2,0,1) correspond to t=0 and r=(0,2,1) correspond to t=1/3.

Now go through the detailed solution attached, you'll be able to understand easily.

Thus Arclength L= units.

Ally Wells answered 10 months ago

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