# The area of the region bounded by the curves $\dpi{100} y=\left | x-1 \right |and\; y=3-\left | x \right |\; is$ Option 1) 3 sq. units Option 2) 4 sq. units Option 3) 6 sq. units Option 4) 2 sq. units

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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