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Integral Identities
(Math | Calculus | Integrals | Identities)

Formal Integral Definition:
(integral)(a to b) f(x) dx = lim (d -> 0) (sum) (k=1..n) f(X(k)) (x(k) - x(k-1)) when...

a = x0 < x1 < x2 < ... < xn = b
d = max (x1-x0, x2-x1, ... , xn - x(n-1))
x(k-1) <= X(k) <= x(k)     k = 1, 2, ... , n
(integral)(a to b) F '(x) dx = F(b) - F(a) (Fundamental Theorem for integrals of derivatives)
(integral)a f(x) dx = a(integral) f(x) dx (if a is constant)

(integral)f(x) + g(x) dx = (integral)f(x) dx + (integral)g(x) dx

(integral)(a to b) f(x) dx = (integral)f(x) dx | (a b)

(integral)(a to b) f(x) dx + (integral)(b to c) f(x) dx = (integral)(a to c) f(x) dx

(integral)f(u) du/dx dx = (integral)f(u) du (integration by substitution)

  
 
  

 
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