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