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  1. r = 10uv i - v j + u k A = ∫∫ dS = ∫∫ || ∂r/∂u x ∂r/∂v || dA ... ∂r/∂u = {10v,0,1} ... ∂r/∂v = {10u,-1,0} ... || ∂r/∂u x ∂r/∂v || = √(100(u² + v²) + 1) = ∫∫ √(100(u² + v²) + 1) du...

    1 Answers · Science & Mathematics · 14/12/2010

  2. No. "I" is usually short for electric "current". "J" is usually the square root of negative 1. [edit] Correction...

    1 Answers · Science & Mathematics · 28/10/2009

  3. ...1>. So, a normal n to the surface is n = r_u x r_v = <sin v, -cos v, u>. At (u, v) = (9, π... (√(3)/2)(x - 9/2) + (-1/2)(y - 9√(3)/2) + 9(z - π/3) = 0. I hope this helps!

    1 Answers · Science & Mathematics · 22/07/2015

  4. r(u, v) = ucos(v)i + usin(v)j + v k r_u = <cosv, sinv, 0> r_v = <...sqrt(1+u^2) sqrt(1+u^2) dvdu = double int 1+u^2 dvdu, v = 0 to 5π, u=0 to 2 = 5π int 1+u^2 du = 5π(u+1...

    2 Answers · Education & Reference · 29/04/2013

  5. ...v, u sin v, v), r_u x r_v = (sin v, -cos v, u) ==> ||r_u x r_v|| = sqrt(1 + u^2). So, ∫∫ F dS = ∫(u = 0 to...π) (1 + u^2) dv du = π(u + u^3/3) {for u = 0 to 5} = 140π/3. I hope this helps!

    1 Answers · Science & Mathematics · 13/08/2010

  6. ...v = (1 - 4sin4t) i + 4(cos4t - 1) j + (1 - t²/2) k v = dr/dt, so integrating again r = ∫ [(1 - 4sin4t) i + 4(cos4t - 1) j + (1 - t²/2) k]dt r = (t + cos4t) i + (sin4t - 4t) j + (t - ...

    1 Answers · Science & Mathematics · 20/09/2009

  7. V = M i + N j + R k the formulas are: div V = Mx + Ny + ...

    1 Answers · Science & Mathematics · 05/04/2008

  8. ...letter straight into a WP and convert it into text that I've ever heard of. And if there ...etc). You must do that also on a Mac. (I use the 'esc' key as it is on a corner...

    2 Answers · Computers & Internet · 13/05/2010

  9. ...1 + (u cos v)² + (u sin v)²)) * ||r_u x r_v|| dA = ∫(u = 0 to 2) ∫(v = 0 to π) √(1 + u²...) du = π(u + u³/3) {for u = 0 to 2} = 14π/3. I hope this helps!

    1 Answers · Science & Mathematics · 02/05/2017

  10. ...v(0) = (-sin 0)i + (cos 0)j + Ck = j + k C =1 So, v(t) = (-sin t)i + (cos t)j + k r(t) = (cos t)i + (sin t)j + tk r(0) = (cos 0)i + (sin 0)j + 0k = i r(2...

    1 Answers · Science & Mathematics · 07/03/2008

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