Recent content by zm500

Homework Statement Find the area of the part of the sphere x^2 + y^2 + z^2 = a^2(a > 0constant) that lies inside the cylinder x^2 + y^2 = ax. Homework Equations double integral of the cross product of the vector Ra and Rb with respect to dA. The Attempt at a Solution I tried to parametrize...

So, the bounds for v are 0\leqv\lequ? I don't understand how they got they got the bounds for u and v. I understand we need an expression for v but I don't know how to come up with that or where to start since u = x+y. Also, are we supposed to come up with an expression visually for v by...

How can I plot lines of constant u i thought you can only do that uv plane.

Where would I start?

Homework Statement Let f be continuous on [0,1] and let R be the triangular region with vertices (0,0), (0,1), and (1,0). Show that double integrals of f(x+y) w.r.t dA over region R equals single integral of uf(u) w.r.t du from 0 to 1.Homework Equations jacobian method The Attempt at a...

ooops never mind. I finally got it. So, the final region D in polar coordinates is r-upper: 2cos(theta) r-lower:0 theta-upper:pi/2 theta-lower:0 i just used r = 2cos(theta) to solve for theta bounds.

Wait... I already have the theta bounds: it's 0 to pi. For theta, I just look at the graph.

So, I used x and y trig identities and got this y-upper bound: r(theta) = 2cos(theta) y-lower bound: r(theta) = 0 But How do I get theta bounds?

OOOOH Ok Imma try that.

it's the function of the y interval --> \sqrt{}2x-x^2 I didn't convert it to polar coordinates, I just graphed it using (x,y) coordinates and looked at the boundaries.

Homework Statement Where the region is: D = {(x,y)| 0\leqx\leq2;0\leqy\leq\sqrt{}2x-x^2} Double integral over region D with f(x,y) = \sqrt{}x^2+y^2 and respect to dA Homework Equations Trig. Identities: x = rcos(theta) y = rsin(theta) x^2+y^2 = r^2The Attempt at a Solution First, I graphed...

Thank You Very Much. Reversing order did the trick.

Homework Statement Find the Volume of the given solid Bounded by the cylinders y^2+z^2=4 and x=2y, x=0,z=0 in the first octantHomework Equations double integral over a region D with f(x,y) dAThe Attempt at a Solution I graphed it in a xyz plane and got these intervals D = {(x,y)|...

Thanks!

Homework Statement Find the work done by the force field F(x,y) = x sin(y)i + yj on a particle that moves along on the parabola y = x^2 from (-1,1) to (2,4). Homework Equations Work = line integral of the dot product of Field vector and change in the path The path is parabola equation...