First we divide the interval [0,4] into two subintervals, as usual. On [0,2] we find the value of f at each endpoint of the subinterval and plot the appropriate points. The area of this trapezoid is On [2,4] we find the value of f at each endpoint of the subinterval and plot the appropriate points. The two heights of the trapezoid are f (2) = 5 and f (4) = 17, so the area of this trapezoid is We add the areas of the trapezoids and estimate that the area of R is 6 + 44 = 50. Since the trapezoids cover R and then some, this is an overestimate. Graphed, the trapezoids look like this:
