# Rs Aggarwal Class 12 Some Special integrals PDF

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### What are special integrals?

There are several special types of integrals that are encountered in calculus, including:

1. The definite integral: A definite integral is an integral where the limits of integration are specified. The definite integral of a function f(x) over the interval [a,b] is denoted by ∫b^a f(x)dx. The definite integral is used to calculate the signed area between the function and the x-axis over a specific interval.
2. Improper integrals: An improper integral is an integral where one or both of the limits of integration are infinite or a point at which the integrand is not defined. Improper integrals can be of two types:
• An integral that converges: It means that the integral has a finite value.
• An integral that diverges: It means that the integral does not have a finite value.
1. Multiple integrals: A multiple integral is an integral where the function to be integrated depends on more than one variable. They can be of two types:
• Double Integral: Integrating a function of two variables over a two-dimensional region.
• Triple Integral: Integrating a function of three variables over a three-dimensional region.
1. Line Integrals: A line integral is a type of integral where the function to be integrated is evaluated along a curve, rather than over a region. It is used to calculate the work done by a force along a path or the circulation of a vector field.
2. Surface Integrals: A surface integral is a type of integral where the function to be integrated is evaluated over a surface, rather than over a region. It is used to calculate the flux of a vector field through a surface.
3. Vector Calculus: Vector Calculus is a branch of mathematics that deals with the study of vector fields and the operations on them such as gradient, divergence, curl, and Laplacian.

These are some of the special types of integrals that are commonly encountered in calculus. Each of these integrals has specific methods for evaluating them and specific applications in physics, engineering, and other fields.

CH-14-Some-Special-integrals

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