Integration Rules Pdf

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Useful derivative and integral formulas kalkulus pelajaran

Useful Derivative And Integral Formulas Kalkulus Pelajaran

We de ne the integral of f x from ato bto be Z b a f x dx lim n 1 Xn i 1 f x i x 2 2 2 provided this limit exists and is independent of the choice of sample points x i If the limist exists we say that f is integrable The following names are given to the parts of the integral Z b z a integral sign f x z integrand z dx integrate Basic integration formulas 1. k dx = kx + C xn+1 2. xndx = + C n + 1 1 3. dx = ln |x| + C x 4. ex dx = ex + C 5. axdx ax = + C ln(a) 6. sin(x) dx = − cos(x) + C 7. cos(x) dx = sin(x) + C 8. sec2(x) dx = tan(x) + C 9. csc2(x) dx = − cot(x) + C 10. sec(x) tan(x) dx = sec(x) + C 11. csc(x) cot(x) dx = − csc(x) + C (any number k) (n 6= −1)

Integration rules sheet

Integration Rules Sheet

Integration Rules PdfHyperbolic Integrals: ∫sech2(𝑥) 𝑥=tanh(𝑥) ∫csch2(𝑥 ) 𝑥=−coth(𝑥 ∫cosh(𝑥) 𝑥=sinh(𝑥) ∫sinh(𝑥) 𝑥=cosh(𝑥) ∫csch(𝑥) 𝑥=ln(tanh(𝑥 2)) ∫sec (𝑥) 𝑥=ln(tan𝑥)+sec(𝑥)) Integrals of Special Functions: ∫cos(𝑥 2𝜋 2) 𝑥=𝐶(𝑥) ∫sin(𝑥) 𝑥 Integration Rules and Techniques Antiderivatives of Basic Functions Power Rule Complete 8 xn 1 Z C n 1 if n 6 1 xn dx ln jxj C if n 1 Exponential Functions With base a Z ax ax dx C ln a With base e this becomes Z ex dx ex C If we have base e and a linear function in the exponent then Z 1 eax b dx eax b C