GRE Subject Test: Math : Simpson's Rule

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

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Example Questions

Example Question #1 : Simpson's Rule

Solve the integral

using Simpson's rule with  subintervals.  

Possible Answers:

Correct answer:

Explanation:

Simpson's rule is 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 9.35.50 pm 

The sum of all the approximation terms is  therefore

Example Question #14 : Functions

Solve the integral

using Simpson's rule with  subintervals.  

Possible Answers:

Correct answer:

Explanation:

Simpson's rule is 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 9.35.58 pm

The sum of all the approximation terms is  therefore

Example Question #3 : Simpson's Rule

Solve the integral

using Simpson's rule with  subintervals.  

Possible Answers:

Correct answer:

Explanation:

Simpson's rule is 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 9.36.10 pm

The sum of all the approximation terms is  therefore

Example Question #2 : Numerical Approximation

Solve the integral

using Simpson's rule with  subintervals.  

Possible Answers:

Correct answer:

Explanation:

Simpson's rule is 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 9.36.20 pm

The sum of all the approximation terms is  therefore

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