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AP® Calculus AB-BC

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A Trigonometric Integral

APCALC-XPWFKE

Evaluate the definite integral, $\int_{0}^{\frac{\pi }{4}}\sec^{2}(x)\ dx$.

A

$\pi$

B

$1$

C

$\cfrac{2}{3}\sqrt{2}$

D

$\cfrac{1}{3}+\cfrac{2}{3}\sqrt{2}$