Integral Calculus or Calculus 2 Crash Course

Topics:

[32] Areas and Distance. 3

[33] The Definite Integral 5

[34] The Fundamental Theorem of Calculus. 6

[35] Physics and Integration. 8

[36] The Substitution Rule. 10

[37] Area Between Curves. 12

[38] Volumes. 14

[39] Volumes by Cylindrical Shells 15

[40] Work. 17

[41] Average Value of a Function. 18

[42] Integration by Parts 19

[43] Trigonometric Integrals. 21

[44] Trigonometric Substitution. 23

[46] Strategy for Integration. 29

[47] Integration Using Tables and Computer Algebra Systems 34

[48] Approximate Integration. 35Trapezoidal Rule. 35Midpoint Rule. 36Simpson’s Rule. 38

[49] Improper Integration. 39

[50] Arclength. 41

[51] Area of a Surface of Revolution. 43

[52] Applications to Physics and Engineering. 44

[53] Applications to Economics and Biology. 45

[54] Probability. 46[55] Modeling with Differential Equations 47

[56] Direction Fields and Euler’s Method. 48

[57] Separable Variables 49

[58] Models for Population Growth. 50

[59] Linear Equations 52

[60] Predator-Prey Systems. 54

[61] Curves Defined by Parametric Equations. 56

[62] Calculus with Parametric Curves 58

[63] Polar Coordinates 59

[64] Arclength in Parametric and Polar 60

[65] Areas and Lengths in Polar Coordinates. 62

[66] Sequences 63

[67] Series 64

[68] The Integral Test and Estimates of Sums. 65

[69] The Comparison Tests 68

[70] Alternating Series 72

[71] Absolute Convergence and the Ratio and Root Tests. 75

[72] Power Series 78

[73] Representations of Functions as Power Series 84

[74] Taylor and Maclaurin Series 85