Answer to Question #164113 in Calculus for Eeshal

Question

Write the Importance of differential and integral in multivariable calculus.

Give at least 10 points.

Answer 1

The integrals of multivariable calculus

 In Mathematics, multivariable calculus or multivariate calculus is an extension of calculus in one variable with functions of several variables. The differentiation and integration process involves multiple variables, rather than once. Let us discuss the definition of multivariable calculus, basic concepts covered in multivariate calculus, applications, and problems in this article.

Multivariable calculus includes six different generalizations of the familiar one-variable integral of a scalar-valued function over an interval. One can integrate functions over one-dimensional curves, two-dimensional planar regions, and surfaces, as well as three-dimensional volumes. When integrating over curves and surfaces, one can integral vector fields, where the one integrates either the tangential (for curves) or the normal (for surfaces) component of the vector field.

On this page, we outline the various integrals, methods you can use to solve them, and their relationship to the fundamental theorems.

The integrals covered in this page are:

• the line integral of a scalar-valued function,
• the line integral of vector fields,
• the surface integral of a scalar-valued function,
• the surface integral of vector fields,
• double integrals, and
• triple integrals.