`int_-1^2(1-x)dx` Evaluate the integral by interpreting it in terms of areas.

`int_-1^2(1-x)dx`

To
interpret the integral in terms of area , graph the integrand.

The integrand
is the function `f(x)=1-x`

Graph the function in the interval (-1,2). Refer
the attached graph.

The bounded region forms two triangles, one triangle
below the x-axis and second triangle above the x-axis.

Area of triangle above
the x-axis `A_2=1/2b_2h_2`

`A_2=1/2*2*2=2`

Area of
triangle below the x-axis `A_1=1/2b_1h_1`

`A_1=1/2*1*1=1/2`

So,`int_-1^2(1-x)dx=A_2-A_1`

`=2-1/2`

`=3/2`

 

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