(1)

Step 1 :

The integral is .

The definite integral is the limit of a sequence of Reimann sums, where we can choose any evalution points we wish.It is usually easiest to write out the formula using right end points.

Integral as summation is defined as where .

In this case

.

, , ...........

Thus, .

The Riemann sum is .

.

Taking the limit of as gives us the exact value of the integral.

Solution:

.

(2)

Step 1 :

The integral is .

The definite integral is the limit of a sequence of Reimann sums, where we can choose any evalution points we wish.It is usually easiest to write out the formula using right end points.

Integral as summation is defined as where .

In this case

.

, , ...........

Thus, .

The Riemann sum is .

.

Solution:

.