GRE Subject Test: Math : Trapezoidal Rule

Example Questions

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 #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 #12 : How To Find 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 #12 : How To Find 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 : Numerical Integration

Evaluate   using the Trapezoidal Rule, with n = 2.