El libro tiene como tema principal el desarrollo de la integral definida en una variable, busca una relación estrecha entre la técnica de integración, la teoría de la integral definida, sus aplicaciones y convergencia. Los ejemplos y problemas refuerzan la teoría desarrollada, están dosificada con fácil acceso para aprender y extender sus resultados a diversas aplicaciones propiciando la investigación.
Los ejemplos están dosificados pensando en el estudiante que no tienen un tutor permanente, y que tranquilamente puede avanzar de lo simple a lo complejo. El objetivo, es motivar la reflexión del lector sobre la capacidad del espíritu humano para hacer abstracciones de la realidad, diseñar construcciones lógico-deductivas con base axiomática, tal como lo hizo Riemann para la integral en el siglo XIX.
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