Concept

Tangent half-angle substitution

Related lectures (32)

Covers integration techniques with a focus on substitution and verification through examples.

Covers changing variables in integrals with a focus on exponential functions.

Compound Functions: Development and Analysis

Covers the development and analysis of compound functions and the importance of analyzing the larger term in power series.

Integration by Substitution

Explores integration by substitution with proofs and examples on anti-derivatives and function equivalence.

Improper integrals: Techniques and Examples

Covers examples of integration by substitution and rational functions.

Improper integrals: Techniques and Examples

Covers improper integrals techniques and examples, exploring convergence and absolute convergence.

Integration Techniques: Change of Variable

Covers the formula for changing variables in integration and explores indefinite integrals with trigonometric substitutions.

Integration Techniques: Change of Variable and Integration by Parts

Explores advanced integration techniques such as change of variable and integration by parts to simplify complex integrals and solve challenging integration problems.

Solving Recurrences: Master Method

Covers the substitution method, Master Theorem, and recursion trees for efficient algorithm analysis.

General Mathematics I - Integration Techniques

Covers integration techniques like parts and substitution with illustrative examples.

Generalized Integrals: Bounded Interval

Introduces generalized integrals on a bounded interval, discussing convergence, divergence, comparison criteria, variable substitution, and corollaries.

Examples of Integrals

Covers various examples of integrals, emphasizing trigonometric substitutions and techniques.

Solving Recurrences and Recursion Trees

Covers techniques for solving recurrences and introduces the Master Theorem.

Fundamental Theorem of Calculus

Covers the fundamental theorem of calculus, immediate integration, and properties of derivatives, with examples of integration by substitution.

Integration Techniques: Partial Integration and Substitution Rule

Covers integration techniques like partial integration and substitution rule, providing step-by-step explanations.

Properties of Integrals: Techniques and Applications

Explores properties of integrals and techniques for calculation.

Change of Variables: Examples

Explores examples of applying the change of variables formula to simplify integrals over different regions in the xy-plane.

Fundamental theorems of calculus and computing techniques

Explores fundamental theorems of calculus and techniques for computation, including integration by parts and substitution.

Avoiding Variable Capture

Explores variable capture in higher-order functions and the importance of variable renaming.

Evaluation and Operators

Explores class evaluation, extension methods, and operator implementation in Scala.