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what is th area enclosed between x =1 and x =5 and f(x) = \ln x ?

  • Option 1)

    \ln 5^{4}

  • Option 2)

    \ln (\frac{5}{e})^{4}

  • Option 3)

    \ln (\frac{5^{5}}{e^4})

  • Option 4)

    \ln\frac{5}{e}

 

Answers (1)

best_answer

As we have learnt,

 

Introduction of area under the curve -

The area between the curve y= f(x),x axis and two ordinates at the point  x=a\, and \,x= b\left ( b>a \right ) is given by

A= \int_{a}^{b}f(x)dx=\int_{a}^{b}ydx

- wherein

 

 \int_{1}^{5} \ln x dx = \left[x\ln x - x \right ]^{5}_{1} = 5\ln 5- 5 - 1\ln 1 +1 = 5\ln 5 -4 = \ln\frac{5^{5}}{e^4}

 


Option 1)

\ln 5^{4}

Option 2)

\ln (\frac{5}{e})^{4}

Option 3)

\ln (\frac{5^{5}}{e^4})

Option 4)

\ln\frac{5}{e}

Posted by

gaurav

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