Question

$\int_{1}^{\sqrt{3}}{\frac{1}{1 + x^{2}}dx}$ is equal to

• A. $\pi ⥂ / ⥂ 12$
• B. $\pi ⥂ / ⥂ 6$
• C. $\pi ⥂ / ⥂ 4$
• D. $\pi ⥂ / ⥂ 3$

Answer 1

Answer: (A)

$\pi ⥂ / ⥂ 12$

Answer 2

$\int_{\mathbf{1}}^{\sqrt{\mathbf{3}}}{\frac{\mathbf{1}}{\mathbf{1 +}\mathbf{x}^{\mathbf{2}}}\mathbf{dx = \lbrack}\mathbf{\tan}^{\mathbf{-}\mathbf{1}}\mathbf{x}\mathbf{\rbrack}_{\mathbf{1}}^{\sqrt{\mathbf{3}}}\mathbf{=}\frac{\mathbf{\pi}}{\mathbf{3}}\mathbf{-}\frac{\mathbf{\pi}}{\mathbf{4}}\mathbf{=}\frac{\mathbf{\pi}}{\mathbf{12}}}$.