Line integrals Use Green’s Theorem to evaluate the following line integrals. Assume all curves are oriented counterclockwise. A sketch is helpful. 38. ∮ c f d y − g d x where 〈 f , g 〉 = 〈 x 〉 and C upper half of the unit circle and the line segment -1 ≤ x ≤ 1, oriented clockwise
Line integrals Use Green’s Theorem to evaluate the following line integrals. Assume all curves are oriented counterclockwise. A sketch is helpful. 38. ∮ c f d y − g d x where 〈 f , g 〉 = 〈 x 〉 and C upper half of the unit circle and the line segment -1 ≤ x ≤ 1, oriented clockwise
Line integrals Use Green’s Theorem to evaluate the following line integrals. Assume all curves are oriented counterclockwise. A sketch is helpful.
38.
∮
c
f
d
y
−
g
d
x
where
〈
f
,
g
〉
=
〈
x
〉
and C upper half of the unit circle and the line segment -1 ≤ x ≤ 1, oriented clockwise
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Line integrals Use Green’s Theorem to evaluate the following line integral. Assume all curves are oriented counterclockwise.A sketch is helpful.
Write and evaluate the definite integral that represents the area of the surface generated by revolving the curve about the x-axis.
y =
1
3
x3
The x y-coordinate plane is given. A curve is rotated about the x-axis to form a surface.
The curve is labeled y = (1⁄3)x3.
The curve starts at the origin, goes up and right getting more steep, and ends at the point (3, 9).
2?
3
dx
0
=
University Calculus: Early Transcendentals (4th Edition)
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