Mathematics

Integrals, Riemann Sums #6


categories: mathematics

Hello everyone,

Still lots to do, but a moment of free time came up (it's already gone, but I started, so I'm continuing). This is the last piece (less theoretical), the most extensive one in terms of exercises (lots of doing, little unnecessary talking). Let's go! Here's what's coming:

  1. Integral of a piecewise-defined function.
  2. Definite integral of an absolute value.
  3. Integration by substitution (various examples).
  4. Integrating a rational expression after simplification by polynomial division.
  5. Integrating expressions that lead to arctan(x) and arcsin(x).
  6. Integration by parts.
  7. Integration using partial fraction decomposition.
  8. Improper integrals.


Integral of a piecewise-defined function

integrals of piecewise-defined functions

Definite integral of an absolute value

integrals of functions with an absolute value

Integration by substitution (various examples)

integration by substitution

Integrating a rational expression after simplification by polynomial division

integration after polynomial division

Integrating expressions that lead to arctan(x) and arcsin(x)

integrals leading to arcsin and arctan

Integration by parts

integration by parts

Integration using partial fraction decomposition

integration using partial fraction decomposition

Improper integrals

improper integrals

PS. There won't be another piece after this one. This one contains only the exercises that are most relevant to the topics raised at the beginning (the subtopics). This is the end of the course.



Thank you :)


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