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RedAssigh3[1].1 - After you substitute u make sure that...

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Unit: The Basics of Integration Module: Illustrating Integration by Substitution Integrating Composite Trigonometric Functions by Substitution www.thinkwell.com [email protected] Copyright 2001, Thinkwell Corp. All Rights Reserved. 352 –rev 06/18/2001 Integration by substitution is a technique for finding the antiderivative of a composite function . A composite function is a function that results from first applying one function, then another. If the du -expression is only off by a constant multiple, you can still use integration by substitution by moving that constant out of the integral. This integral involves a composite function : the sine of a complicated expression. If you let u be the inside of the function, notice that du is found surrounding the sine function.
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Unformatted text preview: After you substitute u , make sure that there are nothing remains in terms of x . Recall that the derivative of sin x is –cos x + C. Make sure to replace u with its expression in terms of x . You can check that your answer is correct by taking its derivative. Here is another composite function. Let u be the inside expression. When you find du , you will notice that there is no multiple of 4 in the integrand, just dx . Since 4 is just a constant multiple, solve for dx and substitute that expression into the integrand. You can move 1/4 outside the integrand since it is a constant multiple. After you integrate, make sure to replace u with its expression in terms of x . Take the derivative of your answer to make sure it is correct....
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