Finding integral of a helicoid

[MasterWu77]

Homework Statement

Evaluate $$\int$$$$\int$$ $$\sqrt{1+x^2+y^2}$$ where S is the helicoid: r(u,v) = u cos(v)i + u sin(v)j+vk , with 0$$\leq$$u$$\leq$$1, 0$$\leq$$v$$\leq$$$$\theta$$.

The S is the area that we are trying to find. the area of the integral i guess.

Homework Equations

I know i have to use the $$\varphi$$ ($$\theta$$,$$\phi$$) = (acos$$\theta$$ sin $$\phi$$, asin$$\theta$$ sin $$\phi$$, acos$$\phi$$)

The Attempt at a Solution

we did examples like this in class but I'm not sure where to start off. do i need to change the equation of the integral into sin and cos?

 

[Nick Bruno]

you don't HAVE to use phi(theta,phi), you can do this in cartesian coordinates... but i think it would be easier to use a different coordinate system. ( i would suggest trying spherical?)

Yes, I you have to change the object of the integral if you want to use a different coordinate system because "x" and "y" are normally used for cartesian coordinates. theta and r are used for polar coordinates, theta, r and z are used for cylindrial coordinates, phi, rho, and theta are typically used for spherical coordinates.

All of these are just variables tho and can really be anything. They stand for angles and radii of the problem.

Remeber tho, when you change the coordinate system of your integral you have to apply the jacobian. ie, for cylindrical coordinates, the r dr dtheta is appended to the integral, or sphereical is some other trig with phi and theta.

Hope this helps somewhat...