### All GRE Subject Test: Math Resources

## Example Questions

### Example Question #9 : Definition Of Integral

### Evaluate:

**Possible Answers:**

**Correct answer:**

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 #10 : Definition Of Integral

### Evaluate:

**Possible Answers:**

**Correct answer:**

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 : Sine

Find :

**Possible Answers:**

**Correct answer:**

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: