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  • Confused! kindly explain, Which of the following integral has maxmum value?

Which of the following integral has maxmum value?

  • Option 1)

    \int_{-5}^{5} \ln |x|\;dx

  • Option 2)

    \int_{-5}^{5}| \ln x|\;dx

  • Option 3)

    \int_{0}^{5} \ln x\;dx

  • Option 4)

    2\int_{0}^{5} \ln x\;dx

 

Answers (1)

best_answer

As we have learnt,

 

Properties of Definite Integration -

If f(x) is defined on x\in (a,b) then \left | \int_{a}^{b}f(x)dx \right |\leq \int_{a}^{b}\left | f\left ( x \right ) \right |dx

-

 

 Graph of |lnx| is always above the x-axis.

So its enclosed the maximum area under the curve.

 


Option 1)

\int_{-5}^{5} \ln |x|\;dx

Option 2)

\int_{-5}^{5}| \ln x|\;dx

Option 3)

\int_{0}^{5} \ln x\;dx

Option 4)

2\int_{0}^{5} \ln x\;dx

Posted by

prateek

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