All GRE Subject Test: Math Resources
Example Questions
Example Question #1 : Trapezoidal Rule
Solve the integral
using the trapezoidal approximation with subintervals.
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 #2 : Numerical Integration
Solve the integral
using the trapezoidal approximation with subintervals.
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 #3 : Numerical Integration
Solve the integral
using the trapezoidal approximation with subintervals.
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 #4 : Numerical Integration
Solve the integral
using the trapezoidal approximation with subintervals.
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 : 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:
3) For n = 2:
4) Simplifying:
All GRE Subject Test: Math Resources
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