chap7sec1 - ( ) cos ( ) x a x x dx b xe dx HINTS: 1. You...

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7.1 Integration by Parts Review the integrals shown on page 469 and integration by substitution. Examples:    1 ( ) ( ) (sin )(cos ) x x e e a dx b x x dx + Remember - integration is done by various techniques and is not as straightforward as differentiation. Typically, selecting the proper technique is the most difficult aspect of integration. Large numbers of practice problems is the best solution to the difficulty you may encounter. The integration rule that corresponds to the product rule for differentiation is integration by parts. INTEGRATION BY PARTS.     u dv uv v du = - OBJECT:  select a substitution that yields a  simpler  integral. GENERALLY:  select u = f(x) to be a function that becomes simpler when differentiated (or at least not more  complicated). Examples (Note Example 2 on page 471)     
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Unformatted text preview: ( ) cos ( ) x a x x dx b xe dx HINTS: 1. You must be able to integrate dv. It will often be the most complicated part that fits an integration formula. 2. An application of the formula should produce an integral that is easier (or at least no harder) to integrate. 3. , 0, let and p kx p kx x e dx p u x dv e dx = = 4. (ln ) , 0, let (ln ) and p q q p x x dx p u x dv x dx = = Integration by parts may need to be applied more than once. Note example 3 on page 471. Examples 2 2 3 ( ) sin 2 Requires integration by parts twice. ( ) Think ahead on this one. ( ) sin(ln ) Refer to example 4. ( ) Area bounded by 5ln , ln( ) ( ) Volume using shells from rotati x a x x dx b x e dx c x dx d y x y x x e = = ng about the y-axis , , . : 1 x x y e y e x-= = =...
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This note was uploaded on 01/20/2012 for the course MATH 2057 taught by Professor Estrada during the Fall '08 term at LSU.

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chap7sec1 - ( ) cos ( ) x a x x dx b xe dx HINTS: 1. You...

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