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 #16 : 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 #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 #1 : Trapezoidal Rule

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: