Table of values of an increasing function $\"\"$ is given.

Determine the lower and upper estimates for $\"\"$ .

Lower estimate for increasing function is left end approximation of the function.

Divide the interval $\"\"$ into $\"\"$ subintervals.

Number of subintervals are $\"\"$ .

Width of the interval is : $\"\"$ .

Left end points are $\"\"$ .

Lower estimation for $\"\"$ .

$\"\"$

Substitute corresponding function values in above expression from the table.

$\"\"$

Lower estimation for $\"\"$ is $\"\"$ .

Upper estimate for increasing function is right end approximation of the function.

Right end points are $\"\"$ .

Upper estimation for $\"\"$ .

$\"\"$

Substitute corresponding function values in above expression from the table.

$\"\"$

$\"\"$ .

Upper estimation for $\"\"$ is $\"\"$ .

Lower estimation for $\"\"$ is $\"\"$ .

Upper estimation for $\"\"$ is $\"\"$ .