Let y=y(x) be the solution of the differential equation x (y x ) d y= (y (y x )-x ) d x,-1 x 1, y (1 2 )= 6 Then the area of the region bounded by the curves x=0, x=1 2 and y=y(x) in the upper half plane is :

Let y=y(x) be the solution of the differential equation x (y x ) …

MCQ

Let $y=y(x)$ be the solution of the differential equation

$x \tan \left(\frac{y}{x}\right) d y=\left(y \tan \left(\frac{y}{x}\right)-x\right) d x,-1 \leq x \leq 1, y\left(\frac{1}{2}\right)=\frac{\pi}{6}$

Then the area of the region bounded by the curves $x=0, x=\frac{1}{\sqrt{2}}$ and $y=y(x)$ in the upper half plane is :

A
$\frac{1}{12}(\pi-3)$
B
$\frac{1}{6}(\pi-1)$
C
$\frac{1}{8}(\pi-1)$
D
$\frac{1}{4}(\pi-2)$

✓

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