Math Is Fun Forum

Dharshi

Member

Registered: 2006-10-31

Posts: 56

Please help with these

(1) Set up a double integral to find the volume of the solid S in the first octant that is bounded above by
the surface z = 9 - x^2 - y^2 , below by the xy-plane, and on the sides by the planes x=0 and y=x.

(2) a. Evaluate ∫ ∫ ∫ (x^2 + 2z)dxdydz where T is the region bounded by the planes z=0 and
y + z = 4 and the cylinder y = x^2
b. Set up a triple integral in cylindrical coordinates that gives the volume of the solid bounded
above by the hemisphere z = 2 - x^2 - y^2 and below by the paraboloid z = x^2 + y^2
c. Set up a triple integral in spherical coordinates that gives the volume of the solid that lies
outside the cone z = 3x^2 + 3y^2 and inside the hemisphere z = 4 - x^2 - y^2 .

(3) Evaluate ∫∫ sin( y-x)/(y+x) dxdy where Ω is the region in the first quadrant bounded by the line x + y=1
and x + y=2. (Use the Jacobian with u = y - x and v = y + x)
(4) Calculate h(r)·dr C ∫ where h(x, y) = (6xy - y^3 )i + (4y + 3x^2 - 3xy^2 )j and C is the curve consisting of
the line segment from (0, 0) to (2, 4) and the parabola y = x^2 from (2, 4) to (3, 9).
(5) a.Let h(x, y) = 2xy^3 i + 4x^2 y^2 j . Calculate C∫h(r)·dr  where C is the boundary of the triangular
region in the first quadrant bounded by the x-axis, the line x=1 and the curve y = x^3 .
b. Let g(x, y) = (2xy + e^x - 3)i + (x^2 - y^2 + sin y)j. Calculate C
∫g(r)·dr where C is the ellipse 4x^2 + 9y^2 = 36
c. Use Green's Theorem to find the area enclosed by the asteroid r(u) = cos^3 ui + sin^3 uj, 0 <= u<= 2pi.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Please help with these

Hi Dharshi;

That is a lot of work there. What have you done?

Please read this:

http://www.mathisfunforum.com/viewtopic.php?id=14654

We are happy to help, that does not mean doing all of the work. That is wrong.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.