RedAssigh3[1].3 - expressing tangent in terms of sine and...

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Unit: Techniques of Integration Module: Integrals Involving Powers of Other Trig Functions Integrals of Other Trigonometric Functions Copyright 2001, Thinkwell Corp. All Rights Reserved. 1544 –rev 06/13/2001 Integrate tangent and cotangent by expressing them in terms of sine and cosine and then using u -substitution . Integrate secant and cosecant by multiplying by an expression equal to one. Although many trigonometric functions can be integrated, it is not true that all trig integrals can be evaluated. If you randomly combine different trig factors together, it isn’t likely that the result will be integrable. Those that are usually require some modification before techniques of integration will work on them. The integrals of sine and cosine are usually covered in Calculus I. But did you ever wonder what the integral of tangent is? To solve this integral, start by
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Unformatted text preview: expressing tangent in terms of sine and cosine. Now you can use u-substitution to solve the integral. A lot of mathematicians do not like negative signs in the answers to their integrals. Notice that by using a log property you can move the negative into the exponent. Then you can replace the cosine term with a secant. A similar method can be used to find the integral of cotangent. Expressing secant in terms of cosine doesnt leave a term for the du in a u-substitution. Instead, try multiplying secant by some expression equal to one. This integral might look more complicated, but it can be evaluated by u-substitution. The numerator is exactly the derivative of the denominator. Dont forget to express your final answer in terms of x and not u . Notice that evaluating trig integrals involves knowing a few tricks. The more of these tricks you see, the more integrals you can solve....
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