Question

$∫_1^{\sqrt{3}}\frac{dx}{1+x^2}$ equals

• A. π/3
• B. 2π/3
• C. π/6
• D. π/12

Answer 1

Answer: (D)

π/12

Answer 2

$∫_1^{\sqrt3}\frac{dx}{1+x^2}$=tan-1x=F(x)

By second fundamental theorem of calculus,we obtain

$∫_1^{\sqrt3}1\frac{dx}{1+x^2}=F(√3)-F(1)$

$=tan^{-1}\sqrt3-tan^{-1} 1$

$=\frac{π}{3}-\frac{π}{4}$

$=\frac{π}{12}$

Hence,the correct Answer is D.