All GRE Subject Test: Math Resources
Example Questions
Example Question #1 : Trigonometric Functions
Evaluate:
Evaluating this integral requires use of the "Product to Sum Formulas of Trigonometry":
For:
So for our given integral, we can rewrite like so:
This can be rewritten as two separate integrals and solved using a simple substitution.
Solving each integral individually, we have:
Substituting this into the integral results in:
The other integral is solved the same way:
Substituting this into the integral results in:
Now combining these two statements together results in one of the answer choices:
Example Question #2 : Trigonometric Functions
Evaluate:
This integral can be easily evaluated by following the rules outlined for integrating powers of sine and cosine.
But first a substitution needs to be made:
Now that we've made this substitution, we will use the rules outlined for integrating powers of sine and cosine:
In General:
1. If "m" is odd, then we make the substitution , and we use the identity
.
2. If "n" is odd, then we make the substitution , and we use the identity
.
For our given problem statement we will use the first rule, and alter the integral like so:
Now we need to substitute back into v:
Now we need to substitute back into u, and rearrange to make it look like one of the answer choices:
Example Question #1 : Trigonometric Functions
Find :
Step 1: Draw a triangle..
The short sides have a length of and the hypotenuse has a length of
.
Step 2: Find Sin (Angle A):
Step 3: Rationalize the root at the bottom:
All GRE Subject Test: Math Resources
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