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Unformatted text preview: able to compute both types. The following identities will be given to you on the exam. I might even put more if Im feeling generous! sin 2 x + cos 2 x = 1 tan 2 x + 1 = sec 2 x cos 2 x = 1 2 (1 + cos(2 x )) sin 2 x = 1 2 (1-cos(2 x )) sin(2 x ) = 2 sin( x ) cos( x ) Techniques you need to know: u-substitution. For example, Z x ( x 2 + 1) 3 dx See Stewart 5.5 for more. Integration by parts. For example, Z x sin( x ) dx See Stewart 7.1 for more. Partial fractions. For example, Z x 2 + 3 x 3-2 x 2-3 x dx See Stewart 7.4 for more. Inverse/trigonometric substitutions. For example, Z 1 x 2 x 2-16 dx See Stewart 7.3 for more. Strategy for integrating i.e., identifying which of the above techniques to apply to a given integral and combining the above techniques to compute integrals. See Stewart 7.5. You also need to know about improper integrals. For example Z 2 1 x 2 dx See Stewart 7.8 for more....
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This note was uploaded on 01/21/2012 for the course MATH 3B taught by Professor Shu during the Spring '08 term at UCSB.
- Spring '08