GRE Subject Test: Math : Simpson's Rule

Example Questions

Example Question #1 : Numerical Approximation

Solve the integral

using Simpson's rule with  subintervals.

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.

The sum of all the approximation terms is  therefore

Example Question #2 : Numerical Approximation

Solve the integral

using Simpson's rule with  subintervals.

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.

The sum of all the approximation terms is  therefore

Example Question #3 : Numerical Approximation

Solve the integral

using Simpson's rule with  subintervals.

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.

The sum of all the approximation terms is  therefore

Example Question #4 : Numerical Approximation

Solve the integral

using Simpson's rule with  subintervals.

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.

The sum of all the approximation terms is  therefore