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If $ϕ (x) = \int {(ϕ (x))}^{- 2} d x$ and $ϕ (1) = 0$ then $ϕ (x) =$

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2x−11/4

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Correct option is C

ϕx=∫ϕx−2dxDifferentiate with respect to x⇒ϕ1(x)=[ϕ(x)]−2⇒(ϕ(x))2⋅ϕ'(x)=13(ϕ(x))2ϕ1(x)=3 Integrate, we get [ϕ(x)]3=3x+c Since ϕ(1)=0⇒0=3+c⇒c=−3 Then [ϕ(x)]3=3x−3=3(x−1) Hence ϕ(x)=[3(x−1)]1/3

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If ϕx=∫ϕx−2dx and ϕ1=0 then ϕx=

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

If $ϕ (x) = \int {(ϕ (x))}^{- 2} d x$ and $ϕ (1) = 0$ then $ϕ (x) =$