GRE Subject Test: Math : Trapezoidal Rule

Study concepts, example questions & explanations for GRE Subject Test: Math

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Example Questions

Example Question #1 : Trapezoidal Rule

Solve the integral

using the trapezoidal approximation with  subintervals.  

Possible Answers:

Correct answer:

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.

 Screen shot 2015 06 11 at 8.19.15 pm

The sum of all the approximation terms is , therefore

Example Question #2 : Trapezoidal Rule

Solve the integral

using the trapezoidal approximation with  subintervals.  

Possible Answers:

Correct answer:

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.

 Screen shot 2015 06 11 at 8.32.39 pm

The sum of all the approximation terms is , therefore

Example Question #3 : Trapezoidal Rule

Solve the integral

using the trapezoidal approximation with  subintervals.  

Possible Answers:

Correct answer:

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.

 Screen shot 2015 06 11 at 8.55.34 pm

The sum of all the approximation terms is , therefore

Example Question #17 : Midpoint Riemann Sums

Solve the integral

using the trapezoidal approximation with  subintervals.  

Possible Answers:

Correct answer:

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.

 Screen shot 2015 06 11 at 8.55.45 pm

The sum of all the approximation terms is , therefore

Example Question #4 : Trapezoidal Rule

Evaluate   using the Trapezoidal Rule, with n = 2.

Possible Answers:

Correct answer:

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: 

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