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Find the area of the region enclosed by the curve y = (1/ 1+x2) and it’s asymptote

Find the area of the region enclosed by the curve y =
(1/
1+x2)
and it’s asymptote

Grade:12

1 Answers

Rinkoo Gupta
askIITians Faculty 81 Points
10 years ago
put x=0 in eq we get y=1=> (0,1) in the intersection point of the graph with axis.
eq of the curve is y+yx^2-1=0
Asymptotes parallel to x axis can be get equating to zero the coeff. of highest degree term of x
i.e. y=0
So the limit can be taken as x=0 to infinity
required area=2integral ydx under lim 0 to infinity
=2integral dx/(1+x^2) under lim x=0 to infinity
=2 [Inverse of tanx] lim x=0 to infinity
=2[tan^-1(infinity)-tan^-1(0)]
=2[pi/2-0]
=pi
Thanks & Regards
AskIITians Faculty

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