### All GRE Subject Test: Math Resources

## Example Questions

### Example Question #1 : Trapezoidal Rule

Solve the integral

using the trapezoidal approximation with subintervals.

**Possible Answers:**

**Correct answer:**

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 : Numerical Integration

Solve the integral

using the trapezoidal approximation with subintervals.

**Possible Answers:**

**Correct answer:**

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 Integration

Solve the integral

using the trapezoidal approximation with subintervals.

**Possible Answers:**

**Correct answer:**

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 #4 : Numerical Integration

Solve the integral

using the trapezoidal approximation with subintervals.

**Possible Answers:**

**Correct answer:**

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.

**Possible Answers:**

**Correct answer:**

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:

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