Integration Cheat Sheet - Web integration by parts is a method to find integrals of products: Then () (*) 1 lim i b a n i fxd xx æ• = • ú =â d. ∫ c f ( x) d x = c ∫ f ( x) d x. 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. © 2005 paul dawkins integrals definitions definite integral: © 2005 paul dawkins integrals definitions definite integral: Divide [ab,] into n subintervals of width dx and choose * x i from each interval. ∫ ( f ( x) + g ( x)) d x = ∫ f ( x) d x + ∫ g ( x) d x. Suppose fx( ) is continuous on [ab,]. Suppose fx( ) is continuous on [ab,].
© 2005 paul dawkins integrals definitions definite integral: \int cf (x)dx = c\int f (x)dx ∫ cf (x)dx = c∫ f (x)dx. Then () (*) 1 lim i b a n i fxdxfxx fi¥ = ¥ ò =då. Then () (*) 1 lim i b a n i fxd xx æ• = • ú =â d. Web the constant rule for indefinite integrals: Divide [ab,] into n subintervals of width dx and choose * x i from each interval. \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. ∫ ( f ( x) + g ( x)) d x = ∫ f ( x) d x + ∫ g ( x) d x. The sum rule for indefinite integrals: 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. Suppose fx( ) is continuous on [ab,]. Web integration by parts is a method to find integrals of products: 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. © 2005 paul dawkins integrals definitions definite integral: Suppose fx( ) is continuous on [ab,]. ∫ u d v = u v − ∫ v d u. ∫ c f ( x) d x = c ∫ f ( x) d x.