$\displaystyle\int_1^{\sqrt{3}} \dfrac{dx}{1+x^2}$ equals

Question

Accepted Answer

D. $\dfrac{\pi}{12}$

1. Antiderivative: $	an^{-1}x$.
2. Evaluate: $	an^{-1}\sqrt{3}-	an^{-1}1=\dfrac{\pi}{3}-\dfrac{\pi}{4}$.
3. $=\dfrac{4\pi-3\pi}{12}=\dfrac{\pi}{12}$.
4. Option A forgets to subtract $	an^{-1}1$.
_Source: syllabus Mathematics Ch 7 "Integrals", p.338_

Answer

$\dfrac{\pi}{3}$

Answer

$\dfrac{2\pi}{3}$

Answer

$\dfrac{\pi}{6}$

$\displaystyle\int_1^{\sqrt{3}} \dfrac{dx}{1+x^2}$ equals

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