All GRE Subject Test: Math Resources
Example Questions
Example Question #1 : Numerical Approximation
Solve the integral
using the trapezoidal approximation with  subintervals. Â
 Trapezoidal approximations are solved using the formula
where  is the number of subintervals and
 is the function evaluated at the midpoint.
For this problem, . Â
The value of each approximation term is below.
Â
The sum of all the approximation terms is , therefore
Example Question #11 : Differential Functions
Solve the integral
using the trapezoidal approximation with  subintervals. Â
 Trapezoidal approximations are solved using the formula
where  is the number of subintervals and
 is the function evaluated at the midpoint.
For this problem, . Â
The value of each approximation term is below.
Â
The sum of all the approximation terms is , therefore
Example Question #11 : Midpoint Riemann Sums
Solve the integral
using the trapezoidal approximation with  subintervals. Â
 Trapezoidal approximations are solved using the formula
where  is the number of subintervals and
 is the function evaluated at the midpoint.
For this problem, . Â
The value of each approximation term is below.
Â
The sum of all the approximation terms is , therefore
Example Question #2 : Numerical Approximation
Solve the integral
using the trapezoidal approximation with  subintervals. Â
 Trapezoidal approximations are solved using the formula
where  is the number of subintervals and
 is the function evaluated at the midpoint.
For this problem, . Â
The value of each approximation term is below.
Â
The sum of all the approximation terms is , therefore
Example Question #9 : Numerical Integration
Evaluate   using the Trapezoidal Rule, with n = 2.
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:Â
3) For n = 2:Â
4) Simplifying:Â
All GRE Subject Test: Math Resources
