Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Concept explainers

Arc Length
Arc length can be thought of as the distance you would travel if you walked along the path of a curve. Arc length is used in a wide range of real applications. We might be interested in knowing how far a rocket travels if it is launched along a parabolic…
Line Integral
A line integral is one of the important topics that are discussed in the calculus syllabus. When we have a function that we want to integrate, and we evaluate the function alongside a curve, we define it as a line integral. Evaluation of a function along…
Triple Integral
Examples:
Question

Let the curve C be the line segment from (0, 0) to (3, 1).

Let F = ⟨2x-y, 4y-x⟩ Calculate the integral

∫c F· dr = ∫c (2x-y)dx + (4y-x)dy 

in two different ways:
(a) Parameterize the curve C and compute the integral directly.

(b) Use the Fundamental Theorem of Line Integrals.

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