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Let \(f\left(x\right)=\int \frac{\sqrt{x}}{(1+x{)}^{2}}dx\). \((x\geq 0)\) Then \(f(3)-f(1)\) is equal to: [JEE Main 202…

Q1

Let \(f\left(x\right)=\int \frac{\sqrt{x}}{(1+x{)}^{2}}dx\). \((x\geq 0)\) Then \(f(3)-f(1)\) is equal to:

[JEE Main 2020, 4 Sep (Shift 1)]

a

\(\frac{\pi }{12}+\frac{1}{2}-\frac{\sqrt{3}}{4}\)

b

\(-\frac{\pi }{6}+\frac{1}{2}+\frac{\sqrt{3}}{4}\)

c

\(-\frac{\pi }{12}+\frac{1}{2}+\frac{\sqrt{3}}{4}\)

d

\(\frac{\pi }{6}+\frac{1}{2}-\frac{\sqrt{3}}{4}\)

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