(a)

Determine  using right endpoints.

Observe the graph of .

Number of subintervals are .

Width of the interval is : .

The subintervals are .

Right end points are  and .

Riemann sum is .

.

Substitute corresponding values of function in above expression observe from the graph.

Area under the graph of the function using right endpoints is .

.

(b)

The graph of function  is given.

Determine  using left end points:

Number of subintervals are .

Width of the interval is  :.

The subintervals are .

Left end points are .

Riemann sum is .

.

Substitute corresponding function values in above expression from the given graph.

Area under the graph of the function using right endpoints is .

.

(c)

Determine  using mid points:

Number of subintervals are .

Width of the interval is  :.

The subintervals are .

Mid points are .

, where .

.

Substitute corresponding function values in above expression from the given graph.

Area under the graph of the function using right endpoints is .

.

(a) Area under the graph of the function using right endpoints is .

(b) Area under the graph of the function using right endpoints is .

(c) Area under the graph of the function using right endpoints is .