(a)

is the area under the graph of an increasing function from to .

is the left end approximation to the area with sub intervals.

is the right end approximation to the area with sub intervals.

Left end approximation is the less than the actual area and right end approximation is larger than the

actual area because the function is increasing.

Therefore, relation among the , and is .

(b)

 Left end and right end approximations are defined as,

and ,

Where width of the interval , and .

(c)

Consider the result in part (a), .

Subtract on each side of the interval.

.

From the part (b), we have .

.

(a) .

(b) .

(c)  .