If , . The area bounded by , -axis, ,…

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

f: [-1, 1] \to \left[-\frac{1}{2}, \frac{1}{2}\right]

f(x) = \frac{x}{1+x^2}

. The area bounded by

y = f^{-1}(x)

X

-axis,

x = \frac{1}{2}

x = -\frac{1}{2}

is (1)

\frac{1}{2} \log e

(2)

\log\left(\frac{e}{2}\right)

(3)

\frac{1}{2} \log \frac{e}{3}

(4)

\frac{1}{2} \log\left(\frac{e}{2}\right)