GRE Subject Test: Math : Trigonometric Integrals

Example Questions

Example Question #9 : 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 #10 : 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 #1 : 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 #2 : 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 #51 : Derivatives & 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 #1 : 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: All GRE Subject Test: Math Resources 