Explain geometrically how the Midpoint Rule is used to approximate a definite integral.

SOLUTIONStep 1In midpoint formula we divide the interval [a,b] into n subintervals of equal width.Therefore we get We shall denote each of the subintervals as Where For each interval let .we then draw the graph for each subinterval with a height of Let us consider a graph with n=6. ApproxDef_G1 We can easily find the area for each of these rectangles using the formula .And therefore for a general we get that Thus the midpoint rule is used to approximate a definite integral.