I need help with a length of the curve question that uses trigonometry (not my best field)

[stiff glacier]

so i have this question on my calc ii class' hw and im really stumped me. first, i applied the fundemental theorum of calc in order to derive that inital equation. then i ser the length formula with that derived equation and, using the double angle property on cos2x, i used the two bounds to get an answer of 1. however, the answer apparently isnt 1. I scanned through my entire work and i dont know what i did wrong. i just got another question like this wrong and i really need to understand this.

[stiff glacier]

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[narrow harness]

hi, the integral is in dt, so d/dx won't undo it

to undo the integral, we need to use d/dt

[stiff glacier]

i dont think this changes much tho because that d/dx was just a writing error

ill still end up with $f'(x) = \sqrt{\cos(2x)}$

[vague grove]

nacho "two sheds" vantas

[stiff glacier]

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