Question:
A. $\frac{\pi}{3}$
B. $\frac{2 \pi}{3}$
C. $\frac{\pi}{6}$
D. $\frac{\pi}{12}$
Solution:
$\int \frac{d x}{1+x^{2}}=\tan ^{-1} x=\mathrm{F}(x)$
By second fundamental theorem of calculus, we obtain
$=\tan ^{-1} \sqrt{3}-\tan ^{-1} 1$
$=\frac{\pi}{3}-\frac{\pi}{4}$
$=\frac{\pi}{12}$
Hence, the correct answer is D.