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Integral Calculus

Integral Calculus

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Integration of Harder Exponential Functions

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Integration of Harder Exponential Functions

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Integral Calculus

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  1. 1 Integration & Logs
  2. 2 Integrating Basic & Reciprocal Trigonometric Functions
  3. 3 Integrating Squared Trigonometric Functions
  4. 4 Calculating Integrals by Differentiation
  5. 5 Integrating (ln x)/x²
  6. 6 Integrating x cos(x)
  7. 7 Anti-Differentiation: Polynomial Functions
  8. 8 Introduction to Primitives
  9. 9 Primitive Functions: Evaluating the Constant
  10. 10 Reverse Chain Rule for Polynomials: Basic Examples
  11. 11 Reverse Chain Rule for Polynomials: Be Careful!
  12. 12 Reverse Chain Rule for Polynomials: General Rules
  13. 13 Primitives of Trigonometric Functions
  14. 14 Primitives of Exponential Functions
  15. 15 Reverse Chain Rule for Trigonometric Functions
  16. 16 Reverse Chain Rule for Rational Functions
  17. 17 The Story of Integration (1 of 4): Areas Under Curves
  18. 18 The Story of Integration (2 of 4): Riemann's Integral
  19. 19 The Story of Integration (3 of 4): The Relation to Derivatives
  20. 20 The Story of Integration (4 of 4): Forming & Evaluating an Integral
  21. 21 Definite & Indefinite Integrals
  22. 22 Integration & Circle Formulas
  23. 23 Relating Integrals & Areas
  24. 24 Integration & Composite Areas
  25. 25 Properties of Definite Integrals: Constant Co-efficients
  26. 26 Properties of Definite Integrals: Even Functions
  27. 27 Symmetrical Areas
  28. 28 Trapezoidal Rule Example
  29. 29 Trapezoidal Rule: Basic Form
  30. 30 Trapezoidal Rule: Multiple Sub-Intervals
  31. 31 Calculating Integrals Indirectly
  32. 32 Tricky Trig/Integration Question (1 of 3)
  33. 33 Tricky Trig/Integration Question (2 of 3)
  34. 34 Tricky Trig/Integration Question (3 of 3)
  35. 35 Another Tricky Trig/Integral Question
  36. 36 Separating Rational Functions for Integration
  37. 37 Integrating Exponential Functions
  38. 38 Integrating Trigonometric Functions (1 of 4): The Basics
  39. 39 Integrating Trigonometric Functions (2 of 4): Involving Chain Rule
  40. 40 Integrating Trigonometric Functions (3 of 4): Involving Identities
  41. 41 Integrating Trigonometric Functions (4 of 4): Involving Symmetrical Areas
  42. 42 Areas Between Curves (example question)
  43. 43 Integrating 2^(lnx)
  44. 44 Area Enclosed Between Trigonometric Graphs
  45. 45 Volume Involving Trigonometric Functions & Identities
  46. 46 Interesting Trig/Calculus Question (1 of 2: Tangents & Areas)
  47. 47 Interesting Trig/Calculus Question (2 of 2: Approximating π with the Squeeze Law)
  48. 48 Properties of Definite Integrals (Establishing various properties of integrals)
  49. 49 Primitive Functions (1 of 4: Introduction and rules of Anti-Differentiation)
  50. 50 Primitive Functions (2 of 4: Importance of the Constant Term in Anti-Differentiation)
  51. 51 Primitive Functions (3 of 4: Limitations to the Anti-Differentiation Formula)
  52. 52 Primitive Functions (4 of 4: Applications of Anti-Differentiation)
  53. 53 Area under Curves (2 of 4: Using Series to generalise Riemann's estimation for area under a curve)
  54. 54 Areas under Curves (1 of 4: Using Rectangles with variable widths to estimate area under curves)
  55. 55 Area under Curves (3 of 4: Where do the components of Riemann's integral come from?)
  56. 56 Area under Curves (4 of 4: Testing Riemann's Integral for areas under simpler relationships)
  57. 57 Area under Curves (Continued) (1 of 2: Relationship between Differentiation and Integration)
  58. 58 Area under Curves (Continued) (2 of 2: Why definite integrals do not take into account the constant)
  59. 59 Integrals & Area (1 of 2: Finding the limitations of Integrals)
  60. 60 Indefinite Integrals (1 of 2: Making Connections with areas and volumes through integrals)
  61. 61 Integrals & Area (2 of 2: Finding Properties of Integrals with Odd and Even Integrands)
  62. 62 Composite Areas (1 of 3: Answering Questions about Area using Integrals)
  63. 63 Indefinite Integrals (2 of 2: Finding the connection between Volumes, Areas and Corner Lengths)
  64. 64 Composite Areas (2 of 3: Finding the Upper and Lower Bounds to solve the question of area)
  65. 65 Composite Areas (3 of 3: Using dy instead of dx to simplify the working to solve the same problem)
  66. 66 Areas Involving Multiple Curves (2 of 4: Finding a general formula to solve for area between curves)
  67. 67 Areas Involving Multiple Curves (1 of 4: Separating the area into two components to solve)
  68. 68 Areas Involving Multiple Curves (3 of 4: Finding Similarities between translated areas)
  69. 69 Areas Involving Multiple Curves (4 of 4: Generalising for a Formula to solve area between curves)
  70. 70 Area Between Two Curves (Solving a 'curve ball' styled question)
  71. 71 Reverse Chain Rule (i.e. Integration via Substitution)
  72. 72 Integrating Exponential Functions (1 of 3: Strategies to find integrals of exponential functions)
  73. 73 Integrating Exponential Functions (2 of 3: Finding the area under exponential curves)
  74. 74 Integrating Exponential Functions (3 of 3: Seeking parallels with Areas of Logarthmic Functions)
  75. 75 Differentiation and Integration of Exponential Functions (Example that combines both)
  76. 76 Integration of Logrithmic Functions (Purpose of the Absolute values in the Integral)
  77. 77 Properties of Definite Integrals (Outline of the Reverse, Dummy and Symmetry properties)
  78. 78 Properties of Definite Integrals (1 of 6: "Round Off" Property of definite integrals)
  79. 79 Properties of Definite Integrals (2 of 6: Outlining the 'Reflective' Property)
  80. 80 Properties of Definite Integrals (3 of 6: Using the Reflective Property to solve an integral)
  81. 81 Properties of Definite Integrals (4 of 6: Outlining the Piecewise and "Limit" Properties)
  82. 82 Properties of Definite Integrals (5 of 6: Using piecewise and limit properties for famous result)
  83. 83 Extension I Quiz (Graphing, Area between curves, Differentiation and Induction)
  84. 84 Rates of Change: Integration (1 of 4: Understanding information from question)
  85. 85 Rates of Change: Integration (2 of 4: Integrating to find v(t) and using it to find Initial Volume)
  86. 86 Rates of Change: Integration (3 of 4: Using the Volume Function to find time of certain events)
  87. 87 Rates of Change: Integration (4 of 4: Finding time to release specific amount of water)
  88. 88 Integrals & Area (Finding the value of the area under an unknown curve)
  89. 89 Introduction to Primitive Functions
  90. 90 Introducing Integration (1 of 4: Considering displacement vs. time)
  91. 91 Introducing Integration (2 of 4: Considering velocity vs. time)
  92. 92 Introducing Integration (3 of 4: Notation)
  93. 93 Introducing Integration (4 of 4: Concrete examples)
  94. 94 Understanding Integration (1 of 2: Different axes, methods of evaluating definite integrals)
  95. 95 Understanding Integration (2 of 2: Signed area)
  96. 96 Properties of Definite Integrals (1 of 4: Sign & symmetry)
  97. 97 Properties of Definite Integrals (2 of 4: Dissection & direction)
  98. 98 Properties of Definite Integrals (3 of 4: Addition)
  99. 99 Properties of Definite Integrals (4 of 4: Piecemeal functions)
  100. 100 Indefinite Integrals (1 of 2: Compared to definite integrals)
  101. 101 Indefinite Integrals (2 of 2: Example questions)
  102. 102 Evaluating Compound Areas (via integration)
  103. 103 Area Between Two Curves - Example (1 of 2: Visualising the region)
  104. 104 Area Between Two Curves - Example (2 of 2: Forming the integral)
  105. 105 Reverse Chain Rule (1 of 3: Standard questions, "Differentiate » integrate" questions)
  106. 106 Reverse Chain Rule (2 of 3: Using a derivative to find a primitive)
  107. 107 Reverse Chain Rule (3 of 3: By explicit substitution)
  108. 108 Integrals & Logarithmic Functions (1 of 2: Deriving the results)
  109. 109 Integrals & Logarithmic Functions (2 of 2: Why are there absolute value signs?)
  110. 110 Identifying a Function from its Derivative
  111. 111 Integrals & Logarithmic Functions - Why does the solution look different?
  112. 112 Applications of Integration & Logarithms
  113. 113 Integration of Harder Exponential Functions
  114. 114 Applications of Integrating Exponential Functions (1 of 2: Evaluating a volume)
  115. 115 Applications of Integrating Exponential Functions (2 of 2: Area beneath a logarithmic curve)
  116. 116 Evaluating Definite Integral with Absolute Value
  117. 117 Interpreting a Graph w/ Calculus (2 of 2: Evaluating an area)
  118. 118 Applications of Trigonometric Integrals (1 of 2: Fundamental properties)
  119. 119 Applications of Trigonometric Integrals (2 of 2: Introductory example)
  120. 120 Integrating with Respect to Time
  121. 121 Primitive Functions (1 of 2: What is anti-differentiation?)
  122. 122 Primitive Functions (2 of 2: Basic example question)
  123. 123 Indefinite Integrals (1 of 4: Review questions & introduction)
  124. 124 Indefinite Integrals (2 of 4: Reverse chain rule)
  125. 125 Indefinite Integrals (3 of 4: When different approaches give different answers)
  126. 126 Indefinite Integrals (4 of 4: Rephrasing primitives from index form)
  127. 127 Integrating Exponential Functions (Basics)
  128. 128 Integrating Trigonometric Functions (1 of 4: Review questions)
  129. 129 Integrating Trigonometric Functions (2 of 4: Establishing basic results)
  130. 130 Integrating Trigonometric Functions (3 of 4: Rearranging to use reverse chain rule)
  131. 131 Integrating Trigonometric Functions (4 of 4: How do we integrate tan x?)
  132. 132 Integrating Exponentials with Other Bases
  133. 133 Logarithms as Primitive Functions (Why are there absolute value signs?)
  134. 134 Fundamental Theorem of Calculus (1 of 5: Considering COVID-19)
  135. 135 Fundamental Theorem of Calculus (2 of 5: Areas under curves)
  136. 136 Fundamental Theorem of Calculus (3 of 5: Relating derivatives & integrals)
  137. 137 Fundamental Theorem of Calculus (4 of 5: Basic examples)
  138. 138 Fundamental Theorem of Calculus (5 of 5: Taking care with negative indices)
  139. 139 Emoji Maths Puzzle (1 of 2: Setting up the problem)
  140. 140 Emoji Maths Puzzle (2 of 2: Evaluating the integral)
  141. 141 Integral Calculus Exam Review (1 of 5: Determining function from gradient)
  142. 142 Integral Calculus Exam Review (2 of 5: Indefinite integrals)
  143. 143 Integral Calculus Exam Review (3 of 5: Reverse chain rule for polynomial)
  144. 144 Integral Calculus Exam Review (4 of 5: Balloon inflation question)
  145. 145 Integral Calculus Exam Review (5 of 5: Proving & using an algebraic identity)
  146. 146 Using Definite Integral Properties
  147. 147 Indefinite Integrals (1 of 3: Simple polynomial examples)
  148. 148 Indefinite Integrals (2 of 3: Basic reverse chain rule examples)
  149. 149 Indefinite Integrals (3 of 3: Harder reverse chain rule examples)
  150. 150 Areas by Integration (1 of 6: Basic area under curve)
  151. 151 Areas by Integration (2 of 6: Area between curve & both axes)
  152. 152 Areas by Integration (3 of 6: Curve enclosing multiple regions)
  153. 153 Areas by Integration (4 of 6: Area by subtraction)
  154. 154 Areas by Integration (5 of 6: Integrating from the y-axis)
  155. 155 Areas by Integration (6 of 6: Area under y = ln x)
  156. 156 Basic Compound Regions (1 of 4: Finding the point of intersection)
  157. 157 Basic Compound Regions (2 of 4: Combining the areas)
  158. 158 Basic Compound Regions (3 of 4: Constructing & interpreting the graph)
  159. 159 Basic Compound Regions (4 of 4: Evaluating the individual integrals)
  160. 160 Areas Between Curves (1 of 3: Establishing "top" minus "bottom")
  161. 161 Areas Between Curves (2 of 3: Evaluating the integrals)
  162. 162 Areas Between Curves (3 of 3: What about beneath the x-axis?)
  163. 163 Curves with Multiple Crossings (1 of 5: Locating the boundaries)
  164. 164 Curves with Multiple Crossings (2 of 5: Combining areas between polynomials)
  165. 165 Curves with Multiple Crossings (3 of 5: Visualising trigonometric functions)
  166. 166 Curves with Multiple Crossings (4 of 5: Symmetry & periodicity in areas)
  167. 167 Curves with Multiple Crossings (5 of 5: Integrating trigonometric functions)
  168. 168 Trapezoidal Rule (1 of 4: Why do we need a method for approximating areas?)
  169. 169 Trapezoidal Rule (2 of 4: Approximating a curve with a polygon)
  170. 170 Trapezoidal Rule (3 of 4: Improving accuracy with multiple shapes)
  171. 171 Trapezoidal Rule (4 of 4: Deriving the general rule for many trapeziums)
  172. 172 Integration Practice (1 of 7: Exponential integrals)
  173. 173 Integration Practice (2 of 7: Trapezoidal rule with exponential function)
  174. 174 Integration Practice (3 of 7: Rational function areas)
  175. 175 Integration Practice (4 of 7: Exponential function area)
  176. 176 Integration Practice (5 of 7: Trigonometric definite integral)
  177. 177 Integration Practice (6 of 7: Trigonometric integral from a derivative)
  178. 178 Integration Practice (7 of 7: Trigonometric/linear enclosed area)
  179. 179 Integral Calculus Q&A (1 of 6: Separating an integrand)
  180. 180 Integral Calculus Q&A (2 of 6: Simple rational functions)
  181. 181 Integral Calculus Q&A (3 of 6: Further rational functions)
  182. 182 Integral Calculus Q&A (4 of 6: Exponential equation reducible to quadratic)
  183. 183 Integral Calculus Q&A (5 of 6: Locating a stationary point)
  184. 184 Integral Calculus Q&A (6 of 6: Further examples)
  185. 185 Integrals and Signed Areas [Exam Question]
  186. 186 Evaluating Constant of Integration (2 of 2: Definite integral)
  187. 187 Evaluating Constant of Integration (1 of 2: Indefinite integral)

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