Question

Evaluate

Integral∫C

(xyplus+yyplus+z)

ds along the curve

r(t)equals=2tiplus+tjplus+(4minus−2t)k,

0less than or equals≤tless than or equals≤1.

Answer #1

Evaluate the line integral R C (x 2 + y 2 ) ds where C is the
line segment from (1, 1) to (2, 5).

Evaluate the line integral, where C is the given
curve.
C
xeyz ds, C is the line segment from
(0, 0, 0) to (3, 4, 2)

Evaluate the line integral, where C is the given
curve.
∫C xyz2 ds, C is the line segment from
(-1,3,0) to (1,4,3)

Evaluate Integral (subscript c) z dx + y dy − x dz, where the
curve C is given by c(t) = t i + sin t j + cost k for 0 ≤ t ≤
π.

Evaluate the surface integral (x+y+z)dS when S is part of the
half-cylinder x^2 +z^2=1, z≥0, that lies between the planes y=0 and
y=2

Evaluate the surface integral.
S
x2yz dS, S is the part of the plane
z = 1 + 2x + 3y
that lies above the rectangle
[0, 4] × [0, 2]

2. Evaluate the double integral Z Z R e ^(x^ 2+y ^2) dA where R
is the semicircular region bounded by x ≥ 0 and x^2 + y^2 ≤ 4.
3. Find the volume of the region that is bounded above by the
sphere x^2 + y^2 + z^2 = 2 and below by the paraboloid z = x^2 +
y^2 .
4. Evaluate the integral Z Z R (12x^ 2 )(y^3) dA, where R is the
triangle with vertices...

Evaluate the surface integral
Evaluate the surface integral
S
F · dS
for the given vector field F and the oriented
surface S. In other words, find the flux of
F across S. For closed surfaces, use the
positive (outward) orientation.
F(x, y, z) = x i + y j + 9 k
S is the boundary of the region enclosed by the
cylinder
x2 + z2 = 1
and the planes
y = 0 and x + y =...

Evaluate the surface integral.
S
(x + y + z) dS, S is the parallelogram with parametric
equations
x = u + v,
y = u − v,
z = 1 + 2u + v,
0 ≤ u ≤ 7,
0 ≤ v ≤ 4.

Evaluate the flux integral ∫ ∫ S F · n dS. F = 〈8, 0, z〉, S is
the boundary of the region bounded above by z = 25 − x2 − y2 and
below by z = 1 (n outward). Enter an exact answer. Do not use
decimal approximations.

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