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  4. The angle of intersection of the curves y =4- x 2 y=x2 is

Q. The angle of intersection of the curves $y =4- x ^{2}$ & $y=x^{2}$ is

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Solution:

given $d y=\left[\left(1+x^{2}\right) \cdot 1+y^{2}\left(1+x^{2}\right)\right] d x=\left(1+y^{2}\right)\left(1+x^{2}\right) d x$
$\therefore \int \frac{d y}{1+y^{2}}=\int\left(1+x^{2}\right) d x$
$ \Rightarrow \tan ^{-1} y=x+x^{3} / 3+c$

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