Important Points related to Methods of Integration
1. Fundamental Theorem of Calculus: This theorem states that the definite integral of a function can be evaluated by finding an antiderivative of the function and subtracting the values at the endpoints of the interval. It connects integration with differentiation.
2. Indefinite Integrals: These are also known as antiderivatives. Finding an indefinite integral involves finding a function whose derivative is the given function. Common techniques include power rule, exponential rule, and trigonometric rules.
3. Integration by Substitution: This technique involves making a substitution to simplify an integral. The substitution is chosen to make the integral more manageable, often by letting a variable equal part of the integrand.
4. Integration by Parts: This method is used to integrate the product of two functions. It is derived from the product rule for differentiation and involves choosing parts of the integrand to differentiate and integrate.
5. Trigonometric Integrals: Special integrals involving trigonometric functions often require trigonometric identities or substitutions. Examples include integrals of sin(x), cos(x), sec(x), and cosec(x) functions.
6. Partial Fractions: When integrating rational functions (ratios of polynomials), you can use partial fraction decomposition to break down the integrand into simpler fractions. This facilitates integration.
Methods of Integration
Methods of Integration in Calculus refer to the various techniques that are used to integrate function easily. Many times it is not possible to directly integrate a function, so we need to use a specific technique to reduce the integral and then perform integration. Any method of integration involves identifying the type of integral and then deciding which method to use.
In this article, we will study what is Integration in calculus, methods of integration mainly the method of substitution, Integration by parts, and Integration using Trigonometric Identities.
Table of Content
- What is Integration in Calculus?
- What are Methods of Integration?
- Integration by Parts
- Example of Integration by Parts
- Integration By Substitution
- Example of Integration by Substitution
- Integration using Trigonometric Identities
- Example of Integration using Trigonometric Identities
- Integration by Partial Fraction
- Example of Integration by Partial Fraction
- Integration of Some Special Functions
- Important Points related to Methods of Integration
- Examples using Methods of Integration
- Practice Problems on Methods of Integration