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Given exxxdxexfxc∫ex(x-1x2)dx=exf(x)+c. Then f(x) satisfying the equation is: - Mathematics

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Question

Given `int "e"^"x" (("x" - 1)/("x"^2)) "dx" = "e"^"x" "f"("x") + "c"`. Then f(x) satisfying the equation is:

Options

  • x

  • x2

  • `1/"x"`

  • None of the above options

MCQ

Solution

`1/"x"`

Explanation:

Given, `int "e"^"x" (("x" - 1)/("x"^2)) "dx" = "e"^"x" "f"("x") + "c"`

Taking L.H.S. = `int "e"^"x" (("x" - 1)/"x"^2) "dx"`

= `int "e"^"x" (1/"x" - 1/"x"^2) "dx"`

= `int "e"^"x". 1/"x" "dx" - int "e"^"x". 1/"x"^2 dx"`

Integrating the first integral by parts taking `1/"x"` as the first function,

= `1/"x". "e"^"x" + int 1/"x"^2. "e"^"x" "dx" - int "e"^"x". 1/"x"^2 "dx" + "c"`

= `1/"x". "e"^"x" + "c"`

On comparing with the R.H.S., we get

f(x) = `1/"x"`

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Definite Integrals
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Q 1.iv
2021-2022 (April) Set 1

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2021-2022 (April) Set 1 (with solutions)
Q 1.iv | 1 mark

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