Fill in the expression which would complete the integral, Mathematics

Fill in the expression which would complete the integral

Consider the spiral given parametrically by

x(t) = 3e^-0.3t sin (6t)
y(t) = 3e^-0.3t cos(6t)

on the interval 0 ≤ t ≤ 6.

976_The spiral.png

a. Fill in the expression which would complete the integral determining the arc length of this spiral on 0 ≤ t ≤ 6.

b. Determine the arc length of the given spiral on 0 ≤ t ≤ 6.

c. Now determine the arc length of the given spiral on [0, ∞).

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Mathematics: Fill in the expression which would complete the integral

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Mathematics: Fill in the expression which would complete the integral

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