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  • Need clarity, kindly explain! - Integral Calculus - JEE Main-12

What is the value of integral F(x) = \int \ln x \; dx, if F(1) = 5 ?

  • Option 1)

    x\ln x -5

  • Option 2)

    x\ln x +5

  • Option 3)

    x\ln x

  • Option 4)

    x\ln x +6

 

Answers (1)

best_answer

As we have learnt,

 

Constant of integration: -

\frac{\mathrm{d} }{\mathrm{d} x}\left ( F\left ( x \right )+C \right )=\frac{\mathrm{d} }{\mathrm{d} x}F \left ( x \right )+0=f\left ( x \right )

Hence    \int f\left ( x \right )dx=F\left ( x \right )+C

- wherein

Where C is the constant of integration .

 

 F(x) = \int \ln x dx = \left [x\ln x - x \right ] + c

F(1) = \left [1\ln 1 - 1 \right ] + c = 5 \Rightarrow c =6

 


Option 1)

x\ln x -5

Option 2)

x\ln x +5

Option 3)

x\ln x

Option 4)

x\ln x +6

Posted by

gaurav

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