# GRE Subject Test: Math : Trapezoidal Rule

## Example Questions

### Example Question #14 : Midpoint Riemann Sums

Solve the integral

using the trapezoidal approximation with  subintervals.

Explanation:

Trapezoidal approximations are 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 #15 : Midpoint Riemann Sums

Solve the integral

using the trapezoidal approximation with  subintervals.

Explanation:

Trapezoidal approximations are 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 : Trapezoidal Rule

Solve the integral

using the trapezoidal approximation with  subintervals.

Explanation:

Trapezoidal approximations are 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 #17 : Midpoint Riemann Sums

Solve the integral

using the trapezoidal approximation with  subintervals.

Explanation:

Trapezoidal approximations are 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 #3 : Numerical Approximation

Evaluate   using the Trapezoidal Rule, with n = 2.