what is the upper bound of error?

Question

Consider the integration if we approximate it through the

trapezoidal rule with n subintervals, what is the upper bound of error?

Answer 1

Step 1:

The integral is .

Number of sub intervals .

Rectangular method is also known as Midpoint method.

Error of bounds for Trapezoidal Rule :

Suppose , for .

If is the error in the trapezoidal rule, then .

Here , and .

Consider .

Apply derivative on each side with respect to x.

Apply derivative on each side with respect to x.

.

Since , .

Therefore, .

Here .

Substitute k = 4, a = 0 and in above expression.

Upper bound of error for the in trapezoidal rule is

Solution :

Upper bound of error for the in trapezoidal rule is