Assume u = u(x) is a differentiable function of x . If n = −1, d dx ( [u(x
Transcription
Assume u = u(x) is a differentiable function of x . If n = −1, d dx ( [u(x
Definition : An antiderivative of a function f is a function F such that F ′(x) = f (x). The indefinite integral of any function f w.r.t. Z x , written f (x) dx , denotes the most general antiderivative of f . If F is any antiderivative of f , then Z f (x) dx = F (x) + C, C constant. Z To integrate f means to find f (x) dx. Z is the integral sign, f (x) is the integrand, C is the constant of integration and x is the variable of integration. Basic integration formulas 1. Z k dx = k x + C, k constant n+1 x 2. xn dx = + C, n 6= −1 n+1 Z Z Z dx 1 −1 dx = = ln x + C, x > 0 3. x dx = x x Z 4. ex dx = ex + C Z 5. Z 6. Z k f (x) dx = k Z f (x) dx, k constant f (x) ± g (x) dx = Z f (x) dx ± Z g (x) dx.