O'Reilly logo

Engineering Mathematics by C. Vijayakumari, P. Sivaramakrishna Das

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

8

Multiple Integrals

8.1 DOUBLE INTEGRATION

Double integrals occur in many practical problems in science and engineering. It is used in problems involving area, volume, mass, centre of mass. In probability theory it is used to evaluate probabilities of two dimensional continuous random variables.

8.1.1 Double Integrals in Cartesian Coordinates

A double integral is defined as the limit of a sum. Let f(x, y) be a continuous function of two independent variables x and y defined in a simple closed region R. Sub-divide R into element areas ΔA1, ΔA2,…, ΔAn by drawing lines parallel to the coordinate axes.

images

Fig. 8.1

Let (xi, yi) be any point in ΔA ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required