Question

Consider integration

Answer 1

Step 1:

The integral is .

Number of sub intervals .

Rectangular method is also known as Midpoint method.

Error of bounds for mid point rule:

Suppose , for .

If is the error in the mid point rule, then .

Here , and .

Consider .

Apply derivative on each side with respect to .

Apply derivative on each side with respect to .

.

Since , .

Therefore, .

Here .

Substitute , and in above expression.

Upper bound for the in rectangular mid point rule is .

Solution :

Upper bound for the in rectangular mid point rule is .