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  • How to solve this problem- - Integral Calculus - JEE Main-10

If f(x)= lnx ; F(x)= \int f(x)dx 

   and   g(x)= F''(x) .

Then G(x)= \int g(x)dx  If   G(1)=5

Find G(x)

 

 

 

 

  • Option 1)

    lnx

  • Option 2)

    lnx+1

  • Option 3)

    lnx+5

  • Option 4)

    lnx+4

 

Answers (1)

best_answer

As we have learned

Rule for integration -

Differentation of the integration of a function is the function itself .

\frac{\mathrm{d} }{\mathrm{d} x}\left [ \int f\left ( x \right )dx \right ]=f\left ( x \right )

-

 

  

Let's solve it step by step 

Since g(x)= \frac{d^{2}}{dx^{2}}\int f(x)dx= \frac{df(x)}{dx}= \frac{d(lnx)}{dx}= 1/x

G(x)= \int 1/x dx = lnx+ C

G(1)= ln1 +C= 5 \Rightarrow C=5


Option 1)

lnx

This is incorrect

Option 2)

lnx+1

This is incorrect

Option 3)

lnx+5

This is correct

Option 4)

lnx+4

This is incorrect

Posted by

gaurav

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