(a)

The definite integral is , .

Let .

Error in Trapezoidal rule:

If  has a continuous second derivative on , then the error approximating the integral  by Trapezoidal Rule is , .

The function .

First derivative is .

Second derivative is .

The second derivative is continuous on the interval .

The maximum value of  on the interval  is .

Approximate error in trapezoidal rule:

Substitute  and .

.

Error in Trapezoidal rule is .

(b)

The definite integral is , .

Error in Simpsons Rule:

If  has a continuous fourth derivative on , then the error approximating the integral  by Simpsons Rule is , .

The function .

First derivative is .

Second derivative is .

Third derivative is .

Fourth derivative is .

The fourth derivative is continuous on the interval .

The maximum value of on the interval  is .

Approximate error in Simpsons rule:

.

Error in Simpsons rule is .

(a) Error in Trapezoidal rule is .

(b) Error in Simpsons rule is .