JAMB 2012 · UTME · Q40

Evaluate $\displaystyle\int_0^{\pi/4} \sec^2\theta\,d\theta$ .

Worked solution (try it first)

$\sec^2\theta$ is the derivative of $\tan\theta$ , so its integral is $\tan\theta$ .
$\left[\tan\theta\right]_0^{\pi/4} = \tan\frac\pi4 - \tan0$
$= 1 - 0$
$= 1$ , option A.