Let and define

MATHEMATICS · Single correct · CBSE · Mathematics · Integrals · Integrals

Problem

Let

f(t)=\dfrac{2t}{1+t^{4}}

and define

g(x)=\displaystyle \int_{1}^{x} f(t)\,dt

. Which of the following is the exact value of

g\bigl(\sqrt{3}\bigr)

? (a)

\arctan 3

(b)

2\Bigl(\arctan 3-\dfrac{\pi}{4}\Bigr)

(c)

\arctan 3-\dfrac{\pi}{4}

(d)

\arctan(\sqrt{3})-\dfrac{\pi}{4}