All GRE Subject Test: Math Resources
Example Questions
Example Question #1 : Integrals
Integrate:
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 #1 : Integrals
Evaluate the following integral:
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 #1 : Integrals
Integrate the following using substitution.
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 #4 : Substitution
Evaluate the following integral:
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
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