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Chandasouk
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http://img2.imageshack.us/img2/5061/14983795.jpg
I have no idea how they simplified the integral to the second step.
I have no idea how they simplified the integral to the second step.
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A line integral is a type of integral used in multivariate calculus to calculate the cumulative effect of a vector function along a curve or path. It represents the area under a curve in a multi-dimensional space.
A line integral is different from a regular integral in that it calculates the cumulative effect of a vector function along a specific path, rather than over a two-dimensional region. It also takes into account the direction of the path, whereas a regular integral does not.
The direction of the path in a line integral is important because it determines the sign of the integral. If the path is traversed in the direction of the vector function, the integral will have a positive value. If the path is traversed in the opposite direction, the integral will have a negative value.
A line integral is calculated by parameterizing the curve or path and then integrating the vector function along the parameterized path. This involves breaking the curve into small segments and calculating the effect of the vector function on each segment, then summing these individual effects to get the total integral.
Line integrals have many applications in physics, engineering, and other fields. They can be used to calculate work done by a force, calculate electric or magnetic flux, and determine the amount of fluid flow through a given path. They are also used in computer graphics to render 3D images and in statistics to calculate probabilities of multi-dimensional events.