# Basic Integration Rules & Problems, Riemann Sum, Area, Sigma Notation, Fundamental Theorem, Calculus

This calculus video tutorial provides examples of basic integration rules with plenty of practice problems. It explains how to find the definite and indefinite integral of polynomial functions, exponenial functions, rational functions, trigonometric functions, and square root / radical functions. It also helps you to find the value of the definite integral / area under the curve using riemann sum – left and right endpoints along with the midpoint rule, trapezoidal rule, and the simpson’s rule. In addition, it explains how to calculate the integral using the limit definition with sigma notation / summation. Finally, this video discusses the fundamental theorem of calculus – part 1 and part 2.

Here is a list of topics:
1. Integration vs Differentiation
2. Antiderivatives and the Indefinite Integral
3. Integrating Constants and Polynomial Functions
4. Integration Techniques – Rewriting, Foiling, Simplifying Fractions, and More.
5. Definite Integral vs Indefinite Integral – What’s the Difference?
6. Indefinite Integral of Radical Functions / Square Root
7. Antiderivative of Exponential Functions and Rational Functions – Natural Logs
8. Integration of Trigonometric Functions – sin, cos, sec^2, sectan, and more.
9. Trigonometric Identities and Double Angle Formulas
10. Riemann Sum – Left Endpoints vs Right Endpoints
11. Approximate Integration – Midpoint Rule
12. Overestimate vs Underestimate – Over approximation vs Under approximation
13. Numerical Integration – Trapezoidal Rule and Simpson’s Rule
14. Averaging Left and Right Riemann Sum to get the Trapezoidal Rule – Proof / Derivative
15. Initial Condition and Particular Solution Problems
16. Finding f(x) given a point – solving for C – constant of integration
17. Particle Motion Problems – Displacement and Total Distance Given Velocity Function
18. Position, Velocity, and Acceleration Problems
19. Speeding up vs Slowing Down – What’s the difference
20. Finding the area under a curve using the limit definition
21. Definite Integral Using Sigma Notation and Summation
22. Drawing Rectangles to approximate the area under the curve
23. How to draw rectangles for left endpoint, right endpoint and midpoint rule – riemann sum
24. Riemann Sum – Data Table – Even and Uneven Intervals – Trapezoidal Rule, Left and Right Riemann Sum
25. Properties of Definite Integrals
26. Integrating Using Geometric Figures and Shapes
27. Geometry – Definite Integral of a circle, semicircle, triangle, and rectangle
28. Basic Integration – Absolute Value Functions
29. Negative area values
30. Fundamental Theorem of Calculus Part 1 and Part 2
31. The derivative of the definite integral problem