The area bounded by the curves x=y2 and x=(2/1+y2) is

Question

The area bounded by the curves x=y2 and x=(2/1+y2) is (A) π-(2/3) (B) π+(2/3) (C) -π-(2/3) (D) None of these

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/dc866d8b36448886e41545f762a99890-.png" /> Solving curves, we get point of intersections (1, ± 1). Required area =2 ∫ limits01((2/1+y2)-y2) d y=π-(2/3) .

Q. The area bounded by the curves $x = y^{2}$ and $x = \frac{2}{1 + y ^{2}}$ is

$π - \frac{2}{3}$

$π + \frac{2}{3}$

$- π - \frac{2}{3}$

None of these

Solving curves, we get
point of intersections $(1, \pm 1)$ .
Required area
$= 2 0 \int 1 (\frac{2}{1 + y ^{2}} - y^{2}) d y = π - \frac{2}{3} .$

Q. The area bounded by the curves x=y2 and x=1+y22​ is

π−32​

π+32​

−π−32​