# GRE Subject Test: Math : Trapezoidal Rule

## Example Questions

### Example Question #1 : Numerical Integration

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 #11 : Differential Functions

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 #2 : 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 #1 : Numerical Integration

Evaluate using the Trapezoidal Rule, with n = 2.      Explanation:

1) n = 2 indicates 2 equal subdivisions. In this case, they are from 0 to 1, and from 1 to 2.

2) Trapezoidal Rule is: 3) For n = 2: 4) Simplifying: ### All GRE Subject Test: Math Resources 