Integration Cheat Sheet

Integration Cheat Sheet - © 2005 paul dawkins integrals definitions definite integral: \int cf (x)dx = c\int f (x)dx ∫ cf (x)dx = c∫ f (x)dx. ∫ u ( x) v ′ ( x) d x = u ( x) v ( x) − ∫ u ′ ( x) v ( x) d x. ∫ u d v = u v − ∫ v d u. Suppose fx( ) is continuous on [ab,]. Web integration by parts is a method to find integrals of products: ∫ ( f ( x) + g ( x)) d x = ∫ f ( x) d x + ∫ g ( x) d x. Divide [ab,] into n subintervals of width dx and choose * x i from each interval. We can use this method, which can be considered as the reverse product rule , by considering one of the two factors as the derivative of another function. Web the constant rule for indefinite integrals:

\Int (F (X)+ G (X)) Dx = \Int F (X)Dx + \Int G (X)Dx ∫ (F (X)+G(X))Dx = ∫ F (X)Dx+∫ G(X)Dx.

Divide [ab,] into n subintervals of width dx and choose * x i from each interval. Then () (*) 1 lim i b a n i fxdxfxx fi¥ = ¥ ò =då. Divide [ab,] into n subintervals of width d x and choose * xi from each interval. ∫ u ( x) v ′ ( x) d x = u ( x) v ( x) − ∫ u ′ ( x) v ( x) d x.

∫ U D V = U V − ∫ V D U.

© 2005 paul dawkins integrals definitions definite integral: The sum rule for indefinite integrals: ∫ ( f ( x) + g ( x)) d x = ∫ f ( x) d x + ∫ g ( x) d x. Web integration by parts is a method to find integrals of products:

Suppose Fx( ) Is Continuous On [Ab,].

Web the constant rule for indefinite integrals: Then () (*) 1 lim i b a n i fxd xx æ• = • ú =â d. Suppose fx( ) is continuous on [ab,]. ∫ c f ( x) d x = c ∫ f ( x) d x.

© 2005 Paul Dawkins Integrals Definitions Definite Integral:

\int cf (x)dx = c\int f (x)dx ∫ cf (x)dx = c∫ f (x)dx. We can use this method, which can be considered as the reverse product rule , by considering one of the two factors as the derivative of another function.