Evaluate . Which of the following is the exact value of the…

MATHEMATICS · Single correct · A Level · Mathematics · Integration · Integration

Problem

Evaluate

\displaystyle \int_{0}^{\pi/4} \sec^{2}\!\theta\,\sqrt{\tan \theta}\,d\theta

. Which of the following is the exact value of the integral? (a)

\dfrac{1}{3}

(b)

\dfrac{20}{21}

(c)

\dfrac{2}{3}

(d)

\dfrac{3}{4}