IIT JEE , AIEEE Forum - Mathematics , Integral Calculus

deepu_0088

_[0]

^{[infinity](1/2x+1)dx}

deepu_0088

please ans

vkvashistha

First solve the limit as follows :-

_{[t ]}

_[0] (t)^(1/t)_{[ ]}

^{[1/2x + 1 ]}dx

remember x should be treated as constant. After solving limit then solve for integration. If u find any problem I'll ready to solve it for you. Thanks

deepu_0088

please solve it i am not able to understand

deepu_0088

please

nigitha_17

first pf al do u have idea about limit of a sum?

nigitha_17

itz easy to understand if u have idea about otherwise a lill difficult

u cant understand it by a short xplanation given by any of us.

vkvashistha

Sorry friend , I can't able to find it's limit. But I can show u my procedure.

my way to find its limit is based on the below theory :

if lim x---->c [f(x)]^g(x) then => it can be written as : - e^{lim x-->c [f(x) - 1]g(x)}It make convinient to find out limit. But I think the relation I have given, there limit does not exist so answer may be "zero" But not confirmed. I will give u solution after confirming ur outrageous questions to my teacher. Thank You.

deepu_0088

hey i am sorryto say that u r wrong _{[ x]}

_{[0 ]} [g(x)]^{f(x) =e_{[ ]}_{[ ]}} ^[g(x)-1]f(x) only when g(x)-->1 & f(x)--> infinity

deepu_0088

i know that its ans is log 4 but do not know how

amar.gupta

Dear deepu,

please check and confirm the question you have posted.As integration of 1/(2x+1) will be ln(2x+1)/2 which eill be zero when x=0 and tends to infinity when x tends to infinity.

so check it out whether something is missing in the question or you have made some mistake while posting it .

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