Engineering Calculus II-Week 4
Engineering Calculus II-Week 4 MATH 2152
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This 2 page Class Notes was uploaded by Kevin Notetaker on Friday February 19, 2016. The Class Notes belongs to MATH 2152 at East Carolina University taught by Dr. Guglielmo Fucci in Spring 2016. Since its upload, it has received 52 views. For similar materials see Engineering Calculus II in Mathematics (M) at East Carolina University.
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Date Created: 02/19/16
2/20/16 Engineering Calculus II Chapter 7.1 Integration by Parts Let f(x) and g(x) be differentiable functions The equation used for the integration of two functions ' f ( )(x)= f ( )(x)− ∫ f( )g'(x) Tip: Let the function you take the antiderivative of to make the integration easier. Ex. 1 ∫ xcos( )dx f ‘(x) = cos(x) g(x) = x f (x) = sin(x) g ‘(x) = dx Now insert the function that corresponds to the integration equation. Integration Equation is the ( )(x)= f ( )(x)− ∫ f ( )'(x) ∫ xcos( )=xsin( )−∫sin ( )x Compute the Integral with a constant of C xcos x =xsin x +cos x +C ∫ ( ) ( ) ( ) Ex. 2 2 2 ∫ 3x sin(x)dx or 3∫ x sin( )dx 2 f ‘(x) = sin(x) g(x) = 3x f(x) = cos(x) g ‘(x)= 6x Insert the function that corresponds to the integration equation 3 xsin( )=−3 x cos ( )6 xcos( ) ∫ ∫ Since you cannot take the antiderivative of xcos(x) do another integration ∫ xcos( ) f ‘(x) = cos(x) g(x) = x f(x) = sin(x) g ‘(x) = dx ∫ xcos( )=xsinx− ∫in x( ) Substitute for xcos(x) and compute the integral with a constant of C 2/20/16 xsin(x+cos? (x) x sin(x)=−3x cos x +6(¿)+C 3∫¿ ∫ x sin ( )−x cos x ( )sin x ( )os x +( )
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