# GRE Subject Test: Math : Simpson's Rule

## Example Questions

### Example Question #18 : Midpoint Riemann Sums

Solve the integral

using Simpson's rule with  subintervals.

Possible Answers:

Correct answer:

Explanation:

Simpson's rule is solved using the formula

where  is the number of subintervals and  is the function evaluated at the midpoint.

For this problem, .

The value of each approximation term is below.

The sum of all the approximation terms is  therefore

### Example Question #1 : Numerical Approximation

Solve the integral

using Simpson's rule with  subintervals.

Possible Answers:

Correct answer:

Explanation:

Simpson's rule is solved using the formula

where  is the number of subintervals and  is the function evaluated at the midpoint.

For this problem, .

The value of each approximation term is below.

The sum of all the approximation terms is  therefore

### Example Question #20 : Midpoint Riemann Sums

Solve the integral

using Simpson's rule with  subintervals.

Possible Answers:

Correct answer:

Explanation:

Simpson's rule is solved using the formula

where  is the number of subintervals and  is the function evaluated at the midpoint.

For this problem, .

The value of each approximation term is below.

The sum of all the approximation terms is  therefore

### Example Question #21 : Differential Functions

Solve the integral

using Simpson's rule with  subintervals.

Possible Answers:

Correct answer:

Explanation:

Simpson's rule is solved using the formula

where  is the number of subintervals and  is the function evaluated at the midpoint.

For this problem, .

The value of each approximation term is below.

The sum of all the approximation terms is  therefore