Chapter 10 of Differential and Integral Calculus by Florentino T. Feliciano and Mariano B. Uy is a pivotal section for students, as it typically transitions from the basics of integration into its more complex and powerful applications.
By the time a student reaches Chapter 10, they have survived the foundational gauntlet: limits (Chapter 1), continuity (Chapter 2), derivatives of algebraic functions (Chapters 3–5), trigonometric, logarithmic, and exponential functions (Chapters 6–8), and implicit differentiation (Chapter 9). They can compute $dy/dx$ in their sleep. But Chapter 10 asks a disarming question: Now that you can differentiate anything, what is it good for? Chapter 10 of Differential and Integral Calculus by
of one of these methods, such as Integration by Parts or Trigonometric Substitution? By the time a student reaches Chapter 10,
While introduced earlier, Chapter 10 often reinforces Integration by Parts ( of one of these methods, such as Integration
Based on the product rule for differentiation, this method is essential for integrals where the integrand is a product of two different types of functions, such as an algebraic function multiplied by a transcendental one. Partial Fractions: