Chap2 - Chapter 2: Review of one-variable integration...

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Unformatted text preview: Chapter 2: Review of one-variable integration Indefinite Integrals: differentiate F ( x) integrate f ( x) = F '( x) y = f ( x) F ( x) = ∫ f ( x)dx b Definite Integrals: ∫ f ( x)dx a Area under the curve a b F ( x) = F (a) + ∫ f ( x)dx a x Examples of useful integration techniques Tricks of the trade: • • • • • Change of variables Integration by parts Parameters Rescaling the variables Length of curve Examples: ∞ ∫ , 0 ∞ 0 − x4 dx π = ( x 2 + 1) 2 4 ∫ e e −∞ x 1 dx = 2 − ax2 ∞ ∫ = Γ (5 / 4 ) , dx = 0 − ax2 0 e ∫ dx = π a ∫ ∞ −∞ xe ... ...
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This note was uploaded on 11/26/2010 for the course PHYS 290 taught by Professor Staff during the Spring '08 term at Purdue University.

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Chap2 - Chapter 2: Review of one-variable integration...

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