Αποτελέσματα Αναζήτησης
Integrals of Exponential and Logarithmic Functions. ∫ ln x dx = x ln x − x + C. + 1 x. + 1. x ∫ x ln xdx = ln x − + C. 2 + 1 ( n + 1 ) x dx = e x + C ∫.
Integration Rules and Formulas Properties of the Integral: (1) Z b a f(x)dx = Z a b f(x)dx (2) Z a a f(x)dx = 0 (3) Z b a kf(x)dx = k Z b a f(x)dx (4) Z b a [f(x)+g(x)]dx = Z b a f(x)dx+ Z b a g(x)dx (5) Z b a f(x)dx = Z c a f(x)dx+ Z b c f(x)dx (a < c < b) (6) Z b a F0(x)dx = F(b) F(a) (7) d dx Z x a f(t)dt = f(x) (8) d dx Z g(x) a f(t)dt = f ...
A Review: The basic integration formulas summarise the forms of indefinite integrals for may of the functions we have studied so far, and the substitution method helps us use the table below to evaluate more complicated functions involving these basic ones.
Basic differentiation and integration formulas. # 1 Derivatives. Memorize. (xn) = nxn−1 dx. 1. (ln x) = dx x. (ex) = ex dx. (sin x) = cos x dx. (cos x) = − sin x dx. (tan x) = sec2 x dx. (cot x) = − csc2 x dx. (sec x) = sec x tan x dx. (csc x) = − csc x cot x dx. (tan–1 1. x) = dx 1 + x2. (sin–1. 1 dx. x) = p1 − x2. # 2 Antiderivatives.
Differentiation Formulas d dx k = 0 (1) d dx [f(x)±g(x)] = f0(x)±g0(x) (2) d dx [k ·f(x)] = k ·f0(x) (3) d dx [f(x)g(x)] = f(x)g0(x)+g(x)f0(x) (4) d dx f(x) g(x ...
Integration by parts: u dv = uv − v du + C Partial Fractions: to integrate a function like ax+b (x+c)(x+d): Write ax+b (x+c)(x+d) = A (x+c) + B (x+d) = A(x+d)+B(x+c) (x+c)(x+d), so ax+b = A(x+d)+B(x+c)=(A+B)x+(Ad+Bc), so a = A+B and b = Ad+Bc; solve for A and B. The approach for more general denomenator can be found in nearly any calculus ...
Basic Integration Formulas. As with differentiation, there are two types of formulas, formulas for the integrals of specific functions and structural type formulas. Each formula for the derivative of a specific function corresponds to a formula for the derivative of an elementary function.
