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
Let D, be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function. (Use C for the constant of integration.)
D() = 8x + 5
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Calculus 3
Module: Line Integral
Chapter 15 Solutions
University Calculus: Early Transcendentals (3rd Edition)
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