Integral Calculus

Integration & Logs.
Integrating Basic & Reciprocal Trigonometric Functions.
Integrating Squared Trigonometric Functions.
Calculating Integrals by Differentiation.
Integrating (ln x)/x².
Integrating x cos(x).
Anti-Differentiation: Polynomial Functions.
Introduction to Primitives.
Primitive Functions: Evaluating the Constant.
Reverse Chain Rule for Polynomials: Basic Examples.
Reverse Chain Rule for Polynomials: Be Careful!.
Reverse Chain Rule for Polynomials: General Rules.
Primitives of Trigonometric Functions.
Primitives of Exponential Functions.
Reverse Chain Rule for Trigonometric Functions.
Reverse Chain Rule for Rational Functions.
The Story of Integration (1 of 4): Areas Under Curves.
The Story of Integration (2 of 4): Riemann's Integral.
The Story of Integration (3 of 4): The Relation to Derivatives.
The Story of Integration (4 of 4): Forming & Evaluating an Integral.
Definite & Indefinite Integrals.
Integration & Circle Formulas.
Relating Integrals & Areas.
Integration & Composite Areas.
Properties of Definite Integrals: Constant Co-efficients.
Properties of Definite Integrals: Even Functions.
Symmetrical Areas.
Trapezoidal Rule Example.
Trapezoidal Rule: Basic Form.
Trapezoidal Rule: Multiple Sub-Intervals.
Calculating Integrals Indirectly.
Tricky Trig/Integration Question (1 of 3).
Tricky Trig/Integration Question (2 of 3).
Tricky Trig/Integration Question (3 of 3).
Another Tricky Trig/Integral Question.
Separating Rational Functions for Integration.
Integrating Exponential Functions.
Integrating Trigonometric Functions (1 of 4): The Basics.
Integrating Trigonometric Functions (2 of 4): Involving Chain Rule.
Integrating Trigonometric Functions (3 of 4): Involving Identities.
Integrating Trigonometric Functions (4 of 4): Involving Symmetrical Areas.
Areas Between Curves (example question).
Integrating 2^(lnx).
Area Enclosed Between Trigonometric Graphs.
Volume Involving Trigonometric Functions & Identities.
Interesting Trig/Calculus Question (1 of 2: Tangents & Areas).
Interesting Trig/Calculus Question (2 of 2: Approximating π with the Squeeze Law).
Properties of Definite Integrals (Establishing various properties of integrals).
Primitive Functions (1 of 4: Introduction and rules of Anti-Differentiation).
Primitive Functions (2 of 4: Importance of the Constant Term in Anti-Differentiation).
Primitive Functions (3 of 4: Limitations to the Anti-Differentiation Formula).
Primitive Functions (4 of 4: Applications of Anti-Differentiation).
Area under Curves (2 of 4: Using Series to generalise Riemann's estimation for area under a curve).
Areas under Curves (1 of 4: Using Rectangles with variable widths to estimate area under curves).
Area under Curves (3 of 4: Where do the components of Riemann's integral come from?).
Area under Curves (4 of 4: Testing Riemann's Integral for areas under simpler relationships).
Area under Curves (Continued) (1 of 2: Relationship between Differentiation and Integration).
Area under Curves (Continued) (2 of 2: Why definite integrals do not take into account the constant).
Integrals & Area (1 of 2: Finding the limitations of Integrals).
Indefinite Integrals (1 of 2: Making Connections with areas and volumes through integrals).
Integrals & Area (2 of 2: Finding Properties of Integrals with Odd and Even Integrands).
Composite Areas (1 of 3: Answering Questions about Area using Integrals).
Indefinite Integrals (2 of 2: Finding the connection between Volumes, Areas and Corner Lengths).
Composite Areas (2 of 3: Finding the Upper and Lower Bounds to solve the question of area).
Composite Areas (3 of 3: Using dy instead of dx to simplify the working to solve the same problem).
Areas Involving Multiple Curves (2 of 4: Finding a general formula to solve for area between curves).
Areas Involving Multiple Curves (1 of 4: Separating the area into two components to solve).
Areas Involving Multiple Curves (3 of 4: Finding Similarities between translated areas).
Areas Involving Multiple Curves (4 of 4: Generalising for a Formula to solve area between curves).
Area Between Two Curves (Solving a 'curve ball' styled question).
Reverse Chain Rule (i.e. Integration via Substitution).
Integrating Exponential Functions (1 of 3: Strategies to find integrals of exponential functions).
Integrating Exponential Functions (2 of 3: Finding the area under exponential curves).
Integrating Exponential Functions (3 of 3: Seeking parallels with Areas of Logarthmic Functions).
Differentiation and Integration of Exponential Functions (Example that combines both).
Integration of Logrithmic Functions (Purpose of the Absolute values in the Integral).
Properties of Definite Integrals (Outline of the Reverse, Dummy and Symmetry properties).
Properties of Definite Integrals (1 of 6: "Round Off" Property of definite integrals).
Properties of Definite Integrals (2 of 6: Outlining the 'Reflective' Property).
Properties of Definite Integrals (3 of 6: Using the Reflective Property to solve an integral).
Properties of Definite Integrals (4 of 6: Outlining the Piecewise and "Limit" Properties).
Properties of Definite Integrals (5 of 6: Using piecewise and limit properties for famous result).
Extension I Quiz (Graphing, Area between curves, Differentiation and Induction).
Rates of Change: Integration (1 of 4: Understanding information from question).
Rates of Change: Integration (2 of 4: Integrating to find v(t) and using it to find Initial Volume).
Rates of Change: Integration (3 of 4: Using the Volume Function to find time of certain events).
Rates of Change: Integration (4 of 4: Finding time to release specific amount of water).
Integrals & Area (Finding the value of the area under an unknown curve).
Introduction to Primitive Functions.
Introducing Integration (1 of 4: Considering displacement vs. time).
Introducing Integration (2 of 4: Considering velocity vs. time).
Introducing Integration (3 of 4: Notation).
Introducing Integration (4 of 4: Concrete examples).
Understanding Integration (1 of 2: Different axes, methods of evaluating definite integrals).
Understanding Integration (2 of 2: Signed area).
Properties of Definite Integrals (1 of 4: Sign & symmetry).
Properties of Definite Integrals (2 of 4: Dissection & direction).
Properties of Definite Integrals (3 of 4: Addition).
Properties of Definite Integrals (4 of 4: Piecemeal functions).
Indefinite Integrals (1 of 2: Compared to definite integrals).
Indefinite Integrals (2 of 2: Example questions).
Evaluating Compound Areas (via integration).
Area Between Two Curves - Example (1 of 2: Visualising the region).
Area Between Two Curves - Example (2 of 2: Forming the integral).
Reverse Chain Rule (1 of 3: Standard questions, "Differentiate » integrate" questions).
Reverse Chain Rule (2 of 3: Using a derivative to find a primitive).
Reverse Chain Rule (3 of 3: By explicit substitution).
Integrals & Logarithmic Functions (1 of 2: Deriving the results).
Integrals & Logarithmic Functions (2 of 2: Why are there absolute value signs?).
Identifying a Function from its Derivative.
Integrals & Logarithmic Functions - Why does the solution look different?.
Applications of Integration & Logarithms.
Integration of Harder Exponential Functions.
Applications of Integrating Exponential Functions (1 of 2: Evaluating a volume).
Applications of Integrating Exponential Functions (2 of 2: Area beneath a logarithmic curve).
Evaluating Definite Integral with Absolute Value.
Interpreting a Graph w/ Calculus (2 of 2: Evaluating an area).
Applications of Trigonometric Integrals (1 of 2: Fundamental properties).
Applications of Trigonometric Integrals (2 of 2: Introductory example).
Integrating with Respect to Time.
Primitive Functions (1 of 2: What is anti-differentiation?).
Primitive Functions (2 of 2: Basic example question).
Indefinite Integrals (1 of 4: Review questions & introduction).
Indefinite Integrals (2 of 4: Reverse chain rule).
Indefinite Integrals (3 of 4: When different approaches give different answers).
Indefinite Integrals (4 of 4: Rephrasing primitives from index form).
Integrating Exponential Functions (Basics).
Integrating Trigonometric Functions (1 of 4: Review questions).
Integrating Trigonometric Functions (2 of 4: Establishing basic results).
Integrating Trigonometric Functions (3 of 4: Rearranging to use reverse chain rule).
Integrating Trigonometric Functions (4 of 4: How do we integrate tan x?).
Integrating Exponentials with Other Bases.
Logarithms as Primitive Functions (Why are there absolute value signs?).
Fundamental Theorem of Calculus (1 of 5: Considering COVID-19).
Fundamental Theorem of Calculus (2 of 5: Areas under curves).
Fundamental Theorem of Calculus (3 of 5: Relating derivatives & integrals).
Fundamental Theorem of Calculus (4 of 5: Basic examples).
Fundamental Theorem of Calculus (5 of 5: Taking care with negative indices).
Emoji Maths Puzzle (1 of 2: Setting up the problem).
Emoji Maths Puzzle (2 of 2: Evaluating the integral).
Integral Calculus Exam Review (1 of 5: Determining function from gradient).
Integral Calculus Exam Review (2 of 5: Indefinite integrals).
Integral Calculus Exam Review (3 of 5: Reverse chain rule for polynomial).
Integral Calculus Exam Review (4 of 5: Balloon inflation question).
Integral Calculus Exam Review (5 of 5: Proving & using an algebraic identity).
Using Definite Integral Properties.
Indefinite Integrals (1 of 3: Simple polynomial examples).
Indefinite Integrals (2 of 3: Basic reverse chain rule examples).
Indefinite Integrals (3 of 3: Harder reverse chain rule examples).
Areas by Integration (1 of 6: Basic area under curve).
Areas by Integration (2 of 6: Area between curve & both axes).
Areas by Integration (3 of 6: Curve enclosing multiple regions).
Areas by Integration (4 of 6: Area by subtraction).
Areas by Integration (5 of 6: Integrating from the y-axis).
Areas by Integration (6 of 6: Area under y = ln x).
Basic Compound Regions (1 of 4: Finding the point of intersection).
Basic Compound Regions (2 of 4: Combining the areas).
Basic Compound Regions (3 of 4: Constructing & interpreting the graph).
Basic Compound Regions (4 of 4: Evaluating the individual integrals).
Areas Between Curves (1 of 3: Establishing "top" minus "bottom").
Areas Between Curves (2 of 3: Evaluating the integrals).
Areas Between Curves (3 of 3: What about beneath the x-axis?).
Curves with Multiple Crossings (1 of 5: Locating the boundaries).
Curves with Multiple Crossings (2 of 5: Combining areas between polynomials).
Curves with Multiple Crossings (3 of 5: Visualising trigonometric functions).
Curves with Multiple Crossings (4 of 5: Symmetry & periodicity in areas).
Curves with Multiple Crossings (5 of 5: Integrating trigonometric functions).
Trapezoidal Rule (1 of 4: Why do we need a method for approximating areas?).
Trapezoidal Rule (2 of 4: Approximating a curve with a polygon).
Trapezoidal Rule (3 of 4: Improving accuracy with multiple shapes).
Trapezoidal Rule (4 of 4: Deriving the general rule for many trapeziums).
Integration Practice (1 of 7: Exponential integrals).
Integration Practice (2 of 7: Trapezoidal rule with exponential function).
Integration Practice (3 of 7: Rational function areas).
Integration Practice (4 of 7: Exponential function area).
Integration Practice (5 of 7: Trigonometric definite integral).
Integration Practice (6 of 7: Trigonometric integral from a derivative).
Integration Practice (7 of 7: Trigonometric/linear enclosed area).
Integral Calculus Q&A (1 of 6: Separating an integrand).
Integral Calculus Q&A (2 of 6: Simple rational functions).
Integral Calculus Q&A (3 of 6: Further rational functions).
Integral Calculus Q&A (4 of 6: Exponential equation reducible to quadratic).
Integral Calculus Q&A (5 of 6: Locating a stationary point).
Integral Calculus Q&A (6 of 6: Further examples).
Integrals and Signed Areas [Exam Question].
Evaluating Constant of Integration (2 of 2: Definite integral).
Evaluating Constant of Integration (1 of 2: Indefinite integral).