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Unformatted text preview: Calculus Integration Techniques Aim To introduce different techniques of integration. Learning Outcomes At the end of this section you will be able to: • Understand the process of integration by substitution, • Understand the process of integration by parts. Integration by Substitution When an integrand cannot be evaluated by inspection we require one or more special techniques. The most important of these techniques is the method of substitution , the inverse of the “Chain Rule” used in differentiation. When differentiating a composite function such as y = (3 x- 4) 5 , the chain rule is generally used, i.e. d y d x = d y d u . d u d x , where u = 3 x- 4. Thus, y = (3 x- 4) 5 ⇒ y = u 5 ⇒ dy du = 5 u 4 and d u d x = 3 ⇒ d y d x = d y d u . d u d x = 5 u 4 . 3 = 15 u 4 = 15(3 x- 4) 4 . Integration by substitution is very similar to reversing the chain rule and is used to change an integrand into a form that is easier to integrate....
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This note was uploaded on 04/24/2011 for the course ECON 201 taught by Professor Takrimasyeda during the Fall '08 term at BRAC University.
- Fall '08