Question

calcular A) f(x)=X^2 + 2×K×X + K B) f (X)= X^2 +(K-1) ×X-K

Answer 1

PROPIEDADES. Sean s y t dos funciones escalonadas en [a, b]. 1. Aditiva: Z b a [s(x) + t(x)] dx = Z b a s(x) dx + Z b a t(x) dx. 2. Homog´enea: Z b a k · s(x) dx = k · Z b a s(x) dx. 3. Monoton´ıa: Si s(x) ≤ t(x), ∀x ∈ [a, b], entonces Z b a s(x) dx ≤ Z b a t(x) dx. 4. Uni´on: Si a < c < b, entonces Z b a s(x) dx = Z c a s(x) dx + Z b c s(x) dx. 5. Traslaci´on: ∀c ∈ R, Z b a s(x) dx = Z b+c a+c s(x − c) dx. 6. Cambio de escala: ∀k 6= 0, Z b a s(x) dx = (1/k) Z kb ka s(x/k) dx