We definitely want to know how a surface integral can be calculated and what is it used for and also a surface integral example but first we would want to know how they are defined. Therefore, we need a new kind of integral that can integrate over objects in higher dimensions and for which we need to expand the concept from a line integral to a surface integral. In a line integral, we integrate over a path in a plane which is one dimensional and on the surface integral, we integrate over a surface which can be two dimensional or three dimensional. Now that we know what an integration means, let us not delay in digging what a surface integration means.Ī surface integral is just like a line integral. It allows us to find the area, volumes, central points and displacement. And finally when the rectangles will be infinitely small, our area integral of the shape would be perfect. If we keep making the rectangles thinner and thinner, our approximation of the area integral of the whole irregular shape would become more and more accurate. If we add up the area of all the regular rectangles, we can find the area integral of the irregular shape. So here is an irregular shape divided into regular rectangles of whose area integral is what we desire to calculate. It will be fruitless to understand integration without an example. The two basic operations, where on one hand differentiation helps us to examine the rates of change and on the other hand integration helps us to add up infinitesimal pieces of a whole. Integration and differentiation are the two sides of calculus. To understand surface integral, it is very important to understand what an integral means.
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