# GRE Subject Test: Math : Trigonometric Integrals

## Example Questions

### Example Question #1 : Integrals

Integrate the following.

Explanation:

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.

Explanation:

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.

Explanation:

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.

Explanation:

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

Derivative cannot be found

Explanation:

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:

Explanation:

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: