The easy road: Eliminate the parameter to get the Cartesian equation:

.... (1)

.... (2)

Substitute (1) into (2):

Getting the double derivative should be simple. For the record, you'd then note that and do the substitution. But there's no need to substitute anything on this occassion.

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The hard road:

since .

Therefore:

.

I assume you're familiar with the arc length formula and I assume you can successfully differentiate both x and y with respect to t. That doesn't leave much to have trouble with.

You might note that

after expanding and simplifying. Therefore the integrand in the arc length formula boils down to . Now it should be blue sky all the way.