GRE Subject Test: Math : Substitution

Example Questions

Example Question #1 : Integrals

Integrate:       Explanation:

This problem requires U-Substitution.  Let and find . Notice that the numerator in has common factor of 2, 3, or 6.  The numerator can be factored so that the term can be a substitute. Factor the numerator using 3 as the common factor. Substitute and terms, integrate, and resubstitute the term. Example Question #31 : Derivatives & Integrals

Evaluate the following integral:       Explanation:

To calculate this integral, we could expand that whole binomial, but it would be very time consuming and a bit of a pain. Instead, let's use u substitution:

Given this: We can say that  Then, plug it back into our original expression Evaluate this integral to get Then, replace u with what we substituted it for to get our final answer. Note because this is an indefinite integral, we need a plus c in it. Example Question #3 : Integrals

Integrate the following using substitution.      Explanation: Using substitution, we set which means its derivative is .

Substituting for , and for we have: Now we just integrate: Finally, we remove our substitution to arrive at an expression with our original variable: Example Question #1 : Integrals

Evaluate the following integral:       Explanation:

To calculate this integral, we could expand that whole binomial, but it would be very time consuming and a bit of a pain. Instead, let's use u substitution:

Given this: We can say that  Then, plug it back into our original expression Evaluate this integral to get Then, replace u with what we substituted it for to get our final answer. Note because this is an indefinite integral, we need a plus c in it. All GRE Subject Test: Math Resources 