Calculus II - Integrals, Applications, Polar and Parametric Equations, Sequences and Series

Calculus II - Integrals, Applications, Polar and Parametric Equations, Sequences and Series

Krista King via YouTube Direct link

Integrals - Calculus (KristaKingMath)

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Integrals - Calculus (KristaKingMath)

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Calculus II - Integrals, Applications, Polar and Parametric Equations, Sequences and Series

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  1. 1 Integrals - Calculus (KristaKingMath)
  2. 2 Summation Notation - Finding the Sum (KristaKingMath)
  3. 3 How to find a Riemann sum using LEFT ENDPOINTS (KristaKingMath)
  4. 4 Riemann sums with right endpoints
  5. 5 THE MOST ACCURATE WAY TO DO A RIEMANN SUM (Midpoint rule)
  6. 6 Close only counts in horseshoes, hand grenades, and Riemann sums
  7. 7 Trapezoidal Rule (KristaKingMath)
  8. 8 Simpson's Approximation (KristaKingMath)
  9. 9 Definite Integral (KristaKingMath)
  10. 10 ARE YOU FINDING THE RIGHT AREA?!! Area under vs. area enclosed by a graph
  11. 11 Definite integral of an even function (KristaKingMath)
  12. 12 Definite integral of an odd function (KristaKingMath)
  13. 13 PART 1 OF THE DREADED FUNDAMENTAL THEOREM OF CALCULUS!
  14. 14 PART 2 OF THE FUNDAMENTAL THEOREM OF CALCULUS!
  15. 15 Net change theorem (KristaKingMath)
  16. 16 Indefinite Integrals (KristaKingMath)
  17. 17 Properties of integrals (KristaKingMath)
  18. 18 Find f(x) given f''(x), its second derivative (KristaKingMath)
  19. 19 Find f(x) given f'''(x), its third derivative (KristaKingMath)
  20. 20 Initial Value Problem (KristaKingMath)
  21. 21 Find f given f'' and initial conditions (KristaKingMath)
  22. 22 Solving Integrals (KristaKingMath)
  23. 23 U-Substitution (KristaKingMath)
  24. 24 U-Substitution in Definite Integrals (KristaKingMath)
  25. 25 Integration by Parts (KristaKingMath)
  26. 26 Integration by parts two times (KristaKingMath)
  27. 27 Integration by parts three times (KristaKingMath)
  28. 28 U-substitution with integration by parts (KristaKingMath)
  29. 29 Integration by parts to prove the reduction formula (KristaKingMath)
  30. 30 A TOTALLY DIFFERENT WAY to do integration by parts!
  31. 31 Partial fractions, distinct linear factors (KristaKingMath)
  32. 32 Partial fractions, distinct linear factors, example 2, part 1 of 2 (KristaKingMath)
  33. 33 Partial fractions, distinct linear factors, example 2, part 2 of 2 (KristaKingMath)
  34. 34 Partial fractions, distinct linear factors, example 3 (KristaKingMath)
  35. 35 Partial fractions, repeated linear factors (KristaKingMath)
  36. 36 Using partial fractions with DISTINCT QUADRATIC FACTORS
  37. 37 Partial fractions, distinct quadratic factors, example 2 (KristaKingMath)
  38. 38 Partial fractions, distinct quadratic factors, example 3 (KristaKingMath)
  39. 39 Partial fractions, repeated quadratic factors (KristaKingMath)
  40. 40 Partial fractions, rationalizing substitution (KristaKingMath)
  41. 41 integrating with partial fractions: how to factor difficult denominators (KristaKingMath)
  42. 42 partial fractions, two ways to find the constants (KristaKingMath)
  43. 43 Integrating a trig function using u-substitution!
  44. 44 Trigonometric integrals - sin^mcos^n, odd m (KristaKingMath)
  45. 45 Trigonometric integrals - sin^mcos^n, odd n (KristaKingMath)
  46. 46 Trigonometric integrals - sin^mcos^n, m and n even (KristaKingMath)
  47. 47 Integrals of trigonometric functions, tan^msec^n, odd m (KristaKingMath)
  48. 48 Integrals of trigonometric functions, tan^msec^n, even n (KristaKingMath)
  49. 49 Integrals of trigonometric functions, sin(mx)cos(nx) (KristaKingMath)
  50. 50 Integrals of trigonometric functions, sin(mx)sin(nx) (KristaKingMath)
  51. 51 Integrals of trigonometric functions, cos(mx)cos(nx) (KristaKingMath)
  52. 52 Hyperbolic integrals... pretty much just like trig integrals
  53. 53 Integrals of Inverse Hyperbolic Functions (KristaKingMath)
  54. 54 How to solve EVERY trigonometric substitution problem ever!
  55. 55 Trigonometric substitution with secant (KristaKingMath)
  56. 56 Trigonometric substitution with sine (KristaKingMath)
  57. 57 Trigonometric substitution with tangent (KristaKingMath)
  58. 58 Integral of a quadratic function (KristaKingMath)
  59. 59 improper integrals, case 2 (KristaKingMath)
  60. 60 improper integrals, case 3 (KristaKingMath)
  61. 61 improper integrals, case 5 (KristaKingMath)
  62. 62 COMPARISON THEOREM WILL FINALLY MAKE SENSE!
  63. 63 Integrals using reduction formulas (KristaKingMath)
  64. 64 Applications of Integration (KristaKingMath)
  65. 65 Average Value of a Function Example 1 (KristaKingMath)
  66. 66 Area between curves - dx (KristaKingMath)
  67. 67 Area between curves - dy (KristaKingMath)
  68. 68 Area between curves - sketching (KristaKingMath)
  69. 69 Arc Length (KristaKingMath)
  70. 70 Arc length x=g(y) (KristaKingMath)
  71. 71 Arc length - simpson's rule (KristaKingMath)
  72. 72 Surface Area of Revolution (KristaKingMath)
  73. 73 Surface area of revolution - simpson's rule (KristaKingMath)
  74. 74 Surface of Revolution (KristaKingMath)
  75. 75 Volume of rotation: disk method about the y-axis or x= (KristaKingMath)
  76. 76 Volume of rotation: disk method about the y-axis or x= (KristaKingMath)
  77. 77 Volume of rotation: disk method about the x-axis or y= (KristaKingMath)
  78. 78 Volume of rotation: washer method about the x-axis or y= (KristaKingMath)
  79. 79 Volume of rotation: washer method about y-axis or x= (KristaKingMath)
  80. 80 Volume of rotation: washer method about x-axis or y= (KristaKingMath)
  81. 81 Volume of rotation: cylindrical shells about the y-axis or x= (KristaKingMath)
  82. 82 Volume of rotation: cylindrical shells about the y-axis or x= (KristaKingMath)
  83. 83 Volume of rotation: cylindrical shells about the x-axis or y= (KristaKingMath)
  84. 84 Mean value theorem for integrals (KristaKingMath)
  85. 85 Work done using a rope to lift a weight (KristaKingMath)
  86. 86 Work Done on Elastic Springs (KristaKingMath)
  87. 87 Work Done by a Variable Force (KristaKingMath)
  88. 88 Moments of the system (KristaKingMath)
  89. 89 Moments of the system, x-axis (KristaKingMath)
  90. 90 Center of mass of the system (KristaKingMath)
  91. 91 Center of mass of the system, x-axis (KristaKingMath)
  92. 92 Hydrostatic pressure (KristaKingMath)
  93. 93 Hydrostatic force (KristaKingMath)
  94. 94 Vertical Motion (integration) (KristaKingMath)
  95. 95 Rectilinear Motion (KristaKingMath)
  96. 96 Centroids of Plane Regions (KristaKingMath)
  97. 97 Centroid of the plane - simpson's rule (KristaKingMath)
  98. 98 Area of the triangle with the given vertices (KristaKingMath)
  99. 99 Present and Future Value (KristaKingMath)
  100. 100 Present and Future Value Example 2 (KristaKingMath)
  101. 101 Present and Future Value Example 3 (KristaKingMath)
  102. 102 Present and Future Value Example 4 (KristaKingMath)
  103. 103 Present and Future Value Example 5 (KristaKingMath)
  104. 104 Consumer and Producer Surplus (KristaKingMath)
  105. 105 Probability density functions (KristaKingMath)
  106. 106 Cardiac output (KristaKingMath)
  107. 107 Cardiac output - simpson's rule (KristaKingMath)
  108. 108 Poiseuille's law (KristaKingMath)
  109. 109 Theorem of Pappus (KristaKingMath)
  110. 110 Eliminating the Parameter (KristaKingMath)
  111. 111 Derivative of a parametric curve (KristaKingMath)
  112. 112 Second Derivative of a Parametric Curve (KristaKingMath)
  113. 113 Sketch the parametric curve by plotting points (KristaKingMath)
  114. 114 Tangent line to the parametric curve (KristaKingMath)
  115. 115 Area under the parametric curve (KristaKingMath)
  116. 116 Parametric area under one arc or loop (KristaKingMath)
  117. 117 Volume of Revolution of a Parametric Curve (KristaKingMath)
  118. 118 Parametric arc length (KristaKingMath)
  119. 119 Parametric arc length and the distance traveled by the particle (KristaKingMath)
  120. 120 Parametric arc length, simpson's rule (KristaKingMath)
  121. 121 Parametric Curve - Surface Area of Revolution (KristaKingMath)
  122. 122 Polar coordinates (KristaKingMath)
  123. 123 Converting Polar Coordinates (KristaKingMath)
  124. 124 Converting Rectangular Equations to Polar Equations (KristaKingMath)
  125. 125 Converting Polar Equations to Rectangular Equations (KristaKingMath)
  126. 126 Distance between two polar points (KristaKingMath)
  127. 127 Sketching Polar Curves (KristaKingMath)
  128. 128 Sketching Polar Curves - 2 Examples (KristaKingMath)
  129. 129 Sketching polar curves from cartesian curves (KristaKingMath)
  130. 130 Tangent line to the polar curve (KristaKingMath)
  131. 131 Vertical and horizontal tangent lines to the polar curve (KristaKingMath)
  132. 132 Polar Area (KristaKingMath)
  133. 133 Polar Area Bounded by One Loop (KristaKingMath)
  134. 134 Points of intersection of two polar curves (KristaKingMath)
  135. 135 Area Between Polar Curves (KristaKingMath)
  136. 136 Polar area inside both curves (KristaKingMath)
  137. 137 Arc Length of a Polar Curve (KristaKingMath)
  138. 138 Polar Parametric Curve - Arc Length (KristaKingMath)
  139. 139 Polar Parametric Curve - Surface Area of Revolution (KristaKingMath)
  140. 140 Taking a look at complex numbers in polar form (KristaKingMath)
  141. 141 Let's multiply some complex numbers! (KristaKingMath)
  142. 142 Analytic Geometry - Graph of a Single Point or of No Points (KristaKingMath)
  143. 143 Analytic Geometry - Set of Points Equally Distant from Two Points (KristaKingMath)
  144. 144 Analytic Geometry- Set of Points Unequally Distant from Two Points (KristaKingMath)
  145. 145 Eccentricity and directrix of the conic section (KristaKingMath)
  146. 146 Parabolas -Vertex, Axis, Focus, Directrix (KristaKingMath)
  147. 147 Equation of a parabola (conic section) (KristaKingMath)
  148. 148 Polar equation of the parabola (conic section) (KristaKingMath)
  149. 149 Vertex axis focus directrix of an ellipse (KristaKingMath)
  150. 150 Equation of an ellipse (conic section) (KristaKingMath)
  151. 151 Polar equation of the ellipse (conic section) (KristaKingMath)
  152. 152 Vertex axis focus directrix asymptotes of a hyperbola (KristaKingMath)
  153. 153 Equation of a hyperbola (conic section) (KristaKingMath)
  154. 154 Polar equation of the hyperbola (conic section) (KristaKingMath)
  155. 155 Listing the first terms of the sequence (KristaKingMath)
  156. 156 Calculating the first terms of the sequence (KristaKingMath)
  157. 157 Finding a formula for the general term of the sequence (a_n) (KristaKingMath)
  158. 158 Does the sequence converge or diverge? (KristaKingMath)
  159. 159 Finding the limit of a convergent sequence (KristaKingMath)
  160. 160 Increasing, decreasing and not monotonic sequences (KristaKingMath)
  161. 161 Bounded sequences (KristaKingMath)
  162. 162 Calculating the first terms in a series of partial sums (KristaKingMath)
  163. 163 Sum of the series of partial sums (KristaKingMath)
  164. 164 nth term test, divergence test, zero test (KristaKingMath)
  165. 165 Convergence of a geometric series (KristaKingMath)
  166. 166 Convergence and sum of a geometric series, example 1 (KristaKingMath)
  167. 167 Convergence and sum of a geometric series, example 2 (KristaKingMath)
  168. 168 Convergence and sum of a geometric series, example 3 (KristaKingMath)
  169. 169 Values for which the geometric series converges (KristaKingMath)
  170. 170 Repeating decimal expressed as a ratio of integers (KristaKingMath)
  171. 171 Convergence of a telescoping series (KristaKingMath)
  172. 172 Sum of Telescoping Series (KristaKingMath)
  173. 173 p-Series test for convergence (KristaKingMath)
  174. 174 How to use the INTEGRAL TEST for series
  175. 175 Comparison Test (KristaKingMath)
  176. 176 Limit Comparison Test (KristaKingMath)
  177. 177 Estimating error/remainder of a series (KristaKingMath)
  178. 178 Alternating Series Test - Calculus (KristaKingMath)
  179. 179 Alternating series estimation theorem (KristaKingMath)
  180. 180 Ratio Test - Calculus (KristaKingMath)
  181. 181 Ratio Test with Factorials (KristaKingMath)
  182. 182 Root Test - Calculus (KristaKingMath)
  183. 183 Absolute and conditional convergence (KristaKingMath)
  184. 184 Difference Between Limit and Sum of the Series (KristaKingMath)
  185. 185 Radius of convergence (KristaKingMath)
  186. 186 Interval of Convergence (KristaKingMath)
  187. 187 Interval of Convergence Example 2 (KristaKingMath)
  188. 188 Power series representation, radius and interval of convergence (KristaKingMath)
  189. 189 Power series multiplication (KristaKingMath)
  190. 190 Power series division (KristaKingMath)
  191. 191 Power series differentiation (KristaKingMath)
  192. 192 Using power series to estimate a definite integral (KristaKingMath)
  193. 193 Binomial series (KristaKingMath)
  194. 194 Taylor Polynomial Example 1 PART 1/2 (KristaKingMath)
  195. 195 Taylor Polynomial Example 1 PART 2/2 (KristaKingMath)
  196. 196 Taylor Polynomial Example 2 PART 1/2 (KristaKingMath)
  197. 197 Taylor Polynomial Example 2 PART 2/2 (KristaKingMath)
  198. 198 Finding radius of convergence of a Taylor series (KristaKingMath)
  199. 199 Taylor's inequality (KristaKingMath)
  200. 200 Maclaurin Series (KristaKingMath)
  201. 201 Sum of the maclaurin series (KristaKingMath)
  202. 202 Maclaurin series radius of convergence (KristaKingMath)
  203. 203 Expressing the integral as a power series (KristaKingMath)
  204. 204 Using maclaurin series to estimate an indefinite integral (KristaKingMath)
  205. 205 Maclaurin series to estimate a definite integral (KristaKingMath)
  206. 206 Maclaurin series to evaluate a limit (KristaKingMath)
  207. 207 How to use inverse hyperbolic functions to evaluate integrals
  208. 208 Partial fractions are SPECIAL! (Repeated linear factors)
  209. 209 PARTIAL FRACTIONS example with distinct linear factors
  210. 210 Trig substitution - How to solve?
  211. 211 Present value of a single deposit, compounded continuously - How do you find it?

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