GRE Subject Test: Math : Trigonometric Integrals
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Example Questions
Example Question #5 :Integrals
Integrate the following.
We can integrate the function by using substitution where
Just focus on integratingsinenow:
The last step is to reinsert the substitution:
Example Question #6 :Integrals
Integrate the following.
We can integrate using substitution:
Now we can just focus on integratingcosine:
Once the integration is complete, we can reinsert our substitution:
Example Question #1 :Trigonometric Integrals
Evaluate the following integral.
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
Finally, we reinsert our substitution:
Example Question #2 :Trigonometric Integrals
Evaluate the following integral.
Recall: The trig identity
We can rewrite the integral using the above identity as
We can now solve the integral using substitution
The last step is to reinsert our substitution:
Example Question #1 :Trigonometric Integrals
Fnd the derivative of tan(x) with respect to x or
Derivative cannot be found
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:
1) The 1/2 is a constant, and so is pulled out front.
2)的积分cos (x)是sin (x), by definition.
3) Writing the limits for evaluation:
4) Using the unit circle,
5)Simplifying:
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