Sorry I am new to the forum, I don't know how to type in the integrals and stuff.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

Let S be the portion of the surface y = x^{2}where 0 <= z <= X <= 2. Compute the surface area of S.

2. Relevant equations

r(u,v) = x(u,v)i + y(u,v)j + z(u,v)k

A(S) = integral r_{u}X r_{v}dA

3. The attempt at a solution

My first attempt I did: x = ucosv, y = u^{2}cos^{2}v, and z = ucosv where 0<= u <= 2 and 0 <= v <= 2pi

when I was doing r_{u}X r_{v}, got a lot of sines and cosines but everything canceled out at the end and became 0.

Then I just decided to use x = x, and y = x^{2}where x is from 0 to 2.

but then r_{y}turns out to be 0.

I am not sure how I would do this, most of the problems I have done are z as a function of x and y, but this case z is given but I don't know what to do with it.

Could some one please help me with this? Thank you for your help in advance.

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# Homework Help: Surface area of smooth parametric surface

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