### All GRE Subject Test: Math Resources

## Example Questions

### Example Question #1 : Trigonometric Integrals

Integrate the following.

**Possible Answers:**

**Correct answer:**

We can integrate the function by using substitution where so .

Just focus on integrating *sine* now:

The last step is to reinsert the substitution:

### Example Question #2 : Trigonometric Integrals

Integrate the following.

**Possible Answers:**

**Correct answer:**

We can integrate using substitution:

and so

Now we can just focus on integrating *cosine*:

Once the integration is complete, we can reinsert our substitution:

### Example Question #3 : Trigonometric Integrals

Evaluate the following integral.

**Possible Answers:**

**Correct answer:**

**Recall:** The identity

The integral can be rewritten as

Because of the trig identity above, we can rewrite it in a different way:

Now we can integrate using substitution where and

Finally, we reinsert our substitution:

### Example Question #4 : Trigonometric Integrals

Evaluate the following integral.

**Possible Answers:**

**Correct answer:**

**Recall**: The trig identity

We can rewrite the integral using the above identity as

We can now solve the integral using substitution and

The last step is to reinsert our substitution:

### Example Question #5 : Trigonometric Integrals

Fnd the derivative of tan(x) with respect to x or

**Possible Answers:**

Derivative cannot be found

**Correct answer:**

The is one of the trigonometric integrals that must be memorized.

Other common trig derivatives that should be memorized are:

### Example Question #6 : Trigonometric Integrals

Evaluate:

**Possible Answers:**

**Correct answer:**

1) The 1/2 is a constant, and so is pulled out front.

2) The integral of cos(x) is sin(x), by definition.

3) Writing the limits for evaluation:

4) Using the unit circle, , and .

5)Simplifying: