Whittaker Hodges
10/03/2023 · Elementary School
ntegran: a) \( 5 x \) b) \( a^{2}+b-c \) c) \( \frac{x^{2} y^{3}}{4} \) d) \( 2-x \) e) \( 2 x-3 y^{2} \)
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Step-by-step Solution
Para encontrar las integrales de las funciones dadas, procederemos a calcular cada una de ellas:
a) \( \int 5x \, dx = \frac{5}{2} x^2 + C \)
b) \( \int (a^2 + b - c) \, dx = (a^2 + b - c)x + C \)
c) \( \int \frac{x^2 y^3}{4} \, dx = \frac{y^3}{4} \cdot \frac{x^3}{3} + C = \frac{y^3 x^3}{12} + C \)
d) \( \int (2 - x) \, dx = 2x - \frac{x^2}{2} + C \)
e) \( \int (2x - 3y^2) \, dx = x^2 - 3y^2 x + C \)
Donde \( C \) es la constante de integración.
Quick Answer
a) \( \int 5x \, dx = \frac{5}{2} x^2 + C \)
b) \( \int (a^2 + b - c) \, dx = (a^2 + b - c)x + C \)
c) \( \int \frac{x^2 y^3}{4} \, dx = \frac{y^3 x^3}{12} + C \)
d) \( \int (2 - x) \, dx = 2x - \frac{x^2}{2} + C \)
e) \( \int (2x - 3y^2) \, dx = x^2 - 3y^2 x + C \)
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