Set up, but do not evaluate, two different iterated integrals equal to the given integral. ∬ σ x y z d S , where σ is the portion of the surface y 2 = x between the planes z = 0 , z = 4 , y = 1 , and y = 2.
Set up, but do not evaluate, two different iterated integrals equal to the given integral. ∬ σ x y z d S , where σ is the portion of the surface y 2 = x between the planes z = 0 , z = 4 , y = 1 , and y = 2.
Set up, but do not evaluate, two different iterated integrals equal to the given integral.
∬
σ
x
y
z
d
S
,
where
σ
is the portion of the surface
y
2
=
x
between the planes
z
=
0
,
z
=
4
,
y
=
1
,
and
y
=
2.
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.
Apply Green's Theorem to evaluate the integral.
$(4y + x)
+x)dx + (y + x)dy
C: The circle (x-3)² + (y-2)² = 3
Convert the double integral
to uv-plane where R is the rectangle enclosed by the lines x − y = 0, x - y = 2, x + y = 0 and x + y = 3, using the change of variables
X
; = 1/2 (u + v), y = 1/2 (u − v).
–
O A.
O B.
C.
[[ (x + y)ex²-y² dA
R
O D.
3 2
1
[²²/edudu
-uev dvdu
3
2
[Lue
I
3
uev dudu
2
-=-=-=-ue
uevdvdu
3
2
[³6²
0
1
ueuv dudv
Let C be the closed, piecewise smooth curve formed by traveling in a straight line between the points (0,0,0), (2, 1,5), (1, 1,3),
and back to the origin in that order. Use Stokes' theorem to evaluate the integral.
[[(11xyz)dx + (
11xyz) dx + (6xy) dy + xdz =
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