GRE Subject Test: Math : Trigonometric Integrals

Study concepts, example questions & explanations for GRE Subject Test: Math

varsity tutors app store varsity tutors android store

Example Questions

Example Question #1 : Trigonometric Integrals

Integrate the following.

Possible Answers:

Correct answer:

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.

Possible Answers:

Correct answer:

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.

Possible Answers:

Correct answer:

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.

Possible Answers:

Correct answer:

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

Possible Answers:

Derivative cannot be found

Correct answer:

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: 

Possible Answers:

Correct answer:

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:  

Learning Tools by Varsity Tutors

Incompatible Browser

Please upgrade or download one of the following browsers to use Instant Tutoring: