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Question Number 35325 by Cheyboy last updated on 17/May/18

Sketch the region enclosed by the  curves of y=1/x and y=1/x^2  and  find the area of the region.  plzz help me

Sketchtheregionenclosedbythecurvesofy=1/xandy=1/x2andfindtheareaoftheregion.plzzhelpme

Answered by MJS last updated on 17/May/18

we need the points of intersection  (1/x)=(1/x^2 ) ⇒ x≠0  x^2 −x=0  x(x−1)=0 ⇒ x=1  so we have only one common point in R:  I_1 = ((1),(1) )  there′s no such region  if we consider I_2 = ((∞),(0) )  we can try to calculate  ∫_1 ^∞ ((1/x)−(1/x^2 ))dx=[ln x+(1/x)]_1 ^∞ =ln ∞+(1/∞)−(ln 1+(1/1))=  =∞+0−(0+1)=∞  so no area exists

weneedthepointsofintersection1x=1x2x0x2x=0x(x1)=0x=1sowehaveonlyonecommonpointinR:I1=(11)theresnosuchregionifweconsiderI2=(0)wecantrytocalculateMissing \left or extra \right=+0(0+1)=sonoareaexists

Commented by Cheyboy last updated on 18/May/18

Thank you very much sir

Thankyouverymuchsir

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