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

sanjeev100 , 11 Years ago
Grade 12
anser 1 Answers
Rinkoo Gupta

Last Activity: 11 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
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