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Title: Calculus_Cheat_Sheet_All Author: ptdaw Created Date: 11/2/2022 7:21:57 AM
Integral Substitution \int f\left(g\left(x\right)\right)\cdot g^'\left(x\right)dx=\int f\left(u\right)du,\:\quad u=g\left(x\right) Definite Integrals Rules Definite Integral Boundaries
Indefinite Integrals Rules: ∫Integration By Parts: ′= −∫ ′ ∫Integral of a Constant: ( ) 𝑥=𝑥⋅ ( ) ∫Taking a Constant out: ⋅ (𝑥 ) 𝑥= ⋅∫ 𝑥 𝑥 ∫Sum/Difference Rule: (𝑥 )± (𝑥 𝑥=∫ (𝑥) 𝑥±∫ 𝑥) 𝑥
Calculus Cheat Sheet Visit http://tutorial.math.lamar.edu for a complete set of Calculus notes. © 2005 Paul Dawkins Integrals Definitions Definite Integral: Suppose fx( ) is continuous on [ab,]. Divide [ab,] into n subintervals of width Dx and choose * x i from each interval. Then () (*) 1 lim i b a n i fxd xx Æ• = • Ú =Â D.
1. Common Integrals. 2. Integrals of Rational Functions. 4. Integrals of Logarithmic Functions. 2 ! i ⋅ i ! 5. Integrals of Trig. Functions.
Integrals with Trigonometric Functions Z sinaxdx= 1 a cosax (63) Z sin2 axdx= x 2 sin2ax 4a (64) Z sinn axdx= 1 a cosax 2F 1 1 2; 1 n 2; 3 2;cos2 ax (65) Z sin3 axdx= 3cosax 4a + cos3ax 12a (66) Z cosaxdx=
Integrate the partial fraction decomposition (P.F.D.). For each factor in the denominator we get term(s) in the decomposition according to the following table. If n is odd. Strip one sine out and convert the remaining sines to cosines using sin 2 x = 1 - 2. If m is odd.
Title: Calculus_Cheat_Sheet_All Author: ptdaw Created Date: 12/9/2022 7:11:52 AM
Integral is called convergent if the limit exists and has a finite value and divergent if the limit doesn’t exist or has infinite value. This is typically a Calc II topic.
Cheat Sheet for Integrals 1. u-Substitution For u-substitution, we usually look for a function (which we substitute as u), whose derivative is also present there. For example if the integrand (the function to be integrated) is cos3 xsinx, then the derivative of cosxwhich is sinxis also present (ignore that \ " as it is just the constant -1). So,