Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa

The area of the region enclosed by the curves y=x,x=e,y=1/x  and the positive x-axis is

  • Option 1)

    3/2 square units

  • Option 2)

    5/2 square units

  • Option 3)

    1/2 square units

  • Option 4)

    1 square units

 

Answers (1)

best_answer

As we learnt in 

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_{0}^{1} x\:dx + \int_{1}^{e}\frac{1}{x}dx

\Rightarrow \left [ \frac{x^2}{2} \right ]_{0}^{1}+ \left [ logx \right ]_{1}^{e}

=\frac{1}{2}+ln\ e

=\frac{1}{2}+1= \frac{3}{2} \: sq\: units


Option 1)

3/2 square units

This is correct option

Option 2)

5/2 square units

This is incorrect option

Option 3)

1/2 square units

This is incorrect option

Option 4)

1 square units

This is incorrect option

Posted by

prateek

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2024 Topper: Farmer’s son Gajare Nilkrishna says ‘keep questioning until you understand’
anam-khan

NIT Puducherry Cut-off 2024: Computer Science and Engineering had highest closing rank last year
anam-khan

What after JEE Main results 2024? All you need to know about JEE Adv, CSAB, JoSAA counselling

Latest Question