In Exercises 13−16, find the line integrals along the given path C.
13.
∫
C
(
x
−
y
)
d
x
, where C:
x
=
t
,
y
=
2
t
+
1
, for
0
≤
t
≤
3
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
Ex.2. Prove that the complete integral of the equation
(xp + yq − z)² = 1 + p²+q²
-
is
(ax + by + cz) = (a² + b² + c2) 1/2
.2
Evaluate the line integral xy dx + x-dy, where C is the path going
counterclockwise around the boundary of the rectangle with corners (0,0),(2,0),(2,3),
and (0,3). You can evaluate directly or use Green's theorem. Write the integral(s), but
do not evaluate.
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BIU
Chapter 15 Solutions
University Calculus: Early Transcendentals (4th Edition)
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Fundamental Theorem of Calculus 1 | Geometric Idea + Chain Rule Example; Author: Dr. Trefor Bazett;https://www.youtube.com/watch?v=hAfpl8jLFOs;License: Standard YouTube License, CC-BY