The region in the first quadrant bounded above by and below by for is finite

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Integrals · Applications of Integrals

Problem

The region in the first quadrant bounded above by

y=\dfrac{1}{x^{2}+1}

and below by

y=\dfrac{1}{(x+1)^{2}}

for

x\ge 0

is finite. Determine its exact area. (a)

\dfrac{\pi}{2}+1

(b)

\pi-1

(c)

\dfrac{\pi}{2}-1

(d) Diverges; the area is infinite