All GRE Subject Test: Math Resources
Example Questions
Example Question #1 :Numerical Integration
Solve the integral
using the trapezoidal approximation withsubintervals.
Trapezoidal approximations are solved using the formula
whereis the number of subintervals andis 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 #12 :How To Find Midpoint Riemann Sums
Solve the integral
using the trapezoidal approximation withsubintervals.
Trapezoidal approximations are solved using the formula
whereis the number of subintervals andis 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 :Trapezoidal Rule
Solve the integral
using the trapezoidal approximation withsubintervals.
Trapezoidal approximations are solved using the formula
whereis the number of subintervals andis 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 :Trapezoidal Rule
Solve the integral
using the trapezoidal approximation withsubintervals.
Trapezoidal approximations are solved using the formula
whereis the number of subintervals andis 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 #5 :Trapezoidal Rule
Evaluateusing 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:
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