The integral ∫012x-1dx by interpreting it in terms of areas.
A definite integral can be interpreted as a net area, that is, as a difference of areas;
where A1 is the region above x- axis and below the graph of f, and A2 is the region below x- axis and above the graph of f.
Area of a triangle : A=12bh
where b is the base and h is the height.
The given integral ∫012x-1dx can be interpreted as the area under the graph of
fx= | 2x-1| between x= 0 and x=1 that means sum of the areas of the two shaded triangles.
Now the integral is net area, but the region is above x-axis so we may add the area of two triangles.
By using formula of area of a triangle,
Therefore, the net area is