The integral ∫-4312xdx by interpreting it in terms of areas.
A definite integral can be interpreted as a net area, that is, 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 ∫-4312xdx can be interpreted as the area under the graph of
fx= 12x between x= -4 and x=3
The graph of fx= 12x is shown below
Now, find the integral as the net area of the two triangles
By using the formula of the area of a triangle,
Thus, the value of the original integral is (both regions are above x-axis)