[用功] 求神人幫解向量分析的題目
(1.)Evaluate ∫∫∫fdV , where f(x; y; z) = x + y + z
and R is the region between x^2 + y^2 + z^2 = 1 and x^2 + y^2 + z^2 = 4.
(2.)Evaluate ∫∫∫fdV , where f(x; y; z) = x + y + z
and R is the regionbelow the plane z = 1 and above the paraboloid z = x^2
+ y^2.
(3.)Evaluate ∫∫∫(x-y)dxdydz, where R is the region inside the cylinder
x^2+y^2<=4,
above the plane z = 0, and below the plane z = x^2 + y^2.
(4.)Evaluate ∫∫RdA by the Cavalieri's principle, where R is a ball of r=1，
centered at (1,1,1).
(5.)Find all the extrema of the function f(x,y) = x^2y + xy^2.
(6.)Find all the extrema of the function f(x,y) = log(x^2 + y^2 + 1).
(7.)∫(x - 2y^2 + 1)dx, where C is parameterized by p(t) = (t + 1; t^2-1)
for 0＜= t ＜= 5
(8.)Evaluate∫∫∫[(x^2 + y^2 + z^2)^3/2]dxdydz, where R is the region
bounded by
the spherical surface x^2 + y^2 + z^2 = 16, and three planes: xy-plane,
yz-plane, and xz-plane.
(Note: x、y、z都大於等於0.)
老師說期末考會從裡面幾題考出來，所以懇求神人幫忙，謝謝～
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