Overview
Integration by Substitution :
When
then,
where
and and so
»
substitute
Consider the integration
We notice that is part of the integration.
and substitute in the integrand.
integration
Substitute and .
substitute
Considering the integration :
If it is observed that can be rewritten as
then,
where
and
This method is "integration by substitution".
summary
Integration by Substitution: When
then,
where
and and so
parametric form
Given a function in parametric form and , To proceed with the integration, substitute and . Then, proceed with variable of integration as
summary
Given a function in parametric form and .
substituting and . the means derivative of
This can be integrated.
tan
Integrate
This can be integrated with
cot
Integrate
This can be integrated with
sec
Integrate
This can be integrated with
cosec
Integrate
This can be integrated with
summary
Integration by Substitution
When
then,
where
and and so
»
Outline
The outline of material to learn "Integral Calculus" is as follows.
• Detailed outline of Integral Calculus
→ Application Scenario
→ Integration First Principles
→ Graphical Meaning of Integration
→ Definition of Integrals
→ Fundamental Theorem of Calculus
→ Algebra of Integrals
→ Antiderivatives: Standard results
→ Integration of Expressions
→ Integration by Substitution
→ Integration using Identities
→ Integration by Parts
→ Integration by Partial Fraction
→ Integration: Combination of Methods