## University Calculus: Early Transcendentals (3rd Edition)

$2$
The formula to calculate the arc length is as follows: $L=\int_{c}^{d} \sqrt {1+[f'(x)]^2} dx$ Re-write the equation as follows: $L=\int_{-\pi/4}^{\pi/4} \sec^2 y dy$ Separate the terms and integrate as follows: $L=[ \tan y]_{-\pi/4}^{\pi/4} \\= (\tan \dfrac{\pi}{4} -\tan \dfrac{-\pi}{4} ) \\= 2$