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Find the area enclosed by the curve f(x) = e^{x}\;; \;x=0\;;\;x=5 and the x-axis.

  • Option 1)

    e^{5}

  • Option 2)

    e^{4}

  • Option 3)

    e^{5} -1

  • Option 4)

    \ln5

 

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

 

 Area =  \int_{0}{5}e^{x}dx = \left[e^{x} \right ]^{5}_{0} = e^{5} - 1

 


Option 1)

e^{5}

Option 2)

e^{4}

Option 3)

e^{5} -1

Option 4)

\ln5

Posted by

gaurav

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