What is Integration in Calculus?

What is Integration in Calculus?

Integration can be defined as the summation of values when the number of terms tends to infinity. It is used to unite a part of the whole. Integration is just the reverse of differentiation and has various applications in all spheres such as physics, chemistry, space, engineering, etc....

What are Methods of Integration?

We know that integration is represented using the symbol ∫ over a function f(x) as follows:...

Integration by Parts

This method is used in cases where the function to be integrated is a product of two or more functions. Let f(x) = g(x)h(x), then f(x) can be integrated by parts by using the below formula:...

Integration By Substitution

This method is used when we find it difficult to integrate a function as it is. In this method, a certain term in the function is substituted as a new variable and the whole function is changed to a new function of a new variable. This means that:...

Example of Integration by Substitution

Let us understand it with an example....

Integration using Trigonometric Identities

This method involves integrating the given function by transforming it using trigonometric identities. The value of the given function is substituted using some other function that is derived by using trigonometric identities. To know more about trigonometric identities, please refer to Trigonometric Identities....

Integration by Partial Fraction

If the function to be integrated is of the form f(x) = g(x)/h(x) where g(x) and h(x) are polynomials, then we use the method of partial fraction. There are multiple cases in partial fractions depending upon the type of f(x)....

Example of Integration by Partial Fraction

Let us understand partial fractions with an example....

Integration of Some Special Functions

In Mathematics, we have some special functions which have pre-defined integration formulas. These functions and their integration are shown below:...

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....

Examples using Methods of Integration

Example 1: Solve [Tex]\bold{\int \log x~dx}  [/Tex]....

Practice Problems on Methods of Integration

Problem 1: Calculate the following integrals:...

Methods of Integration – FAQs

What do you mean by integration?...