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  • Need clarity, kindly explain! - Integral Calculus - JEE Main-5

The area of the region bounded by the curves y=\left | x-1 \right |and\; y=3-\left | x \right |\; is

  • Option 1)

    3 sq. units

  • Option 2)

    4 sq. units

  • Option 3)

    6 sq. units

  • Option 4)

    2 sq. 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

 

 y=(x-1) and y=3-(x)

Area=difference of area of \Delta S

=ar\Delta ABC-ar\Delta ADE-ar\Delta EFC

=\frac{1}{2}\times 6\times 3-\frac{1}{2}\times 4\times 2-\frac{1}{2}\times 2\times 1

=9 - 4 - 1 = 4 sq units 


Option 1)

3 sq. units

This option is incorrect 

Option 2)

4 sq. units

This option is correct 

Option 3)

6 sq. units

This option is incorrect 

Option 4)

2 sq. units

This option is incorrect 

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