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1. ### (du/dx)+u+au^(5/4)+u^4=0?

(du/dx)+u+au^(5/4)+u^4 = 0 so (du/dx) = -(u+au^(5/4)+u^4) and thus -du/(u+au^(5/4)+u^4) = dx so we reach the... x(u) to get the desired functional form u(x) Unfortunately, I'm not certain if...

2 Answers · Science & Mathematics · 19/05/2008

2. ### vector component of u orthogonal to a formula?

Let U = A vector = <Ux, Uy, Uz> Let... = A/|A| Let V = The vector projection of U on A is = (U•A)Â U•A = (...

1 Answers · Science & Mathematics · 14/03/2014

3. ### using u substitution integrate?

∫ [x /(10 - √x)] dx = let (10 - √x) = u → √x = 10 - u → square both sides: x = (10 - u)² → dx = 2...3(10)u² - u³] /u} du = distribute and break it into: - 2 ∫ (1000/u) du + 2 ∫ [(300u)/u] du - 2 ∫ [(30u²)/u] du + 2 ∫ (u³/u) du = pull...

1 Answers · Science & Mathematics · 17/02/2009

4. ### If u dot (v x w) = |u||v||w|, show that u dot v = u dot w = v dot w = 0?

By definition u.v x w = |v x w| |u| cosθ where θ is the angle between u and v x w... where Θ is the angle between v and w. So u.v x w = |v||w| sinΘ |u| cosθ and this is equal to |u||v...

2 Answers · Science & Mathematics · 03/10/2009

5. ### U-substitution in algebra?

U-substitution in an algebra class is only representative of simplification. For instance, you can change a part of the equation that has 4xy^2 into U, and simplify the problem using U, and then plug the 4xy^2 into the equation...

4 Answers · Science & Mathematics · 31/07/2006

6. ### Proof that Proj-u-V is orthogonal to Orth-u-V?? ?

I'll let P(u) denote the projection of u along V and O(u) = u - P(u). ...let be the dot product. We want to show, for all w in V, that (O(u),w) = (u-P(u),w) = ((u-v),w) = 0. Well, how do we find v? v ...

1 Answers · Science & Mathematics · 23/01/2009

7. ### find antiderivative u/(16+u^2)?

u du/(16 + u^2) Let w = 16 + u^2 then dw = 2u du so (1/2) dw = u du We now have (1/2) ∫ dw/w = (1/2) ln w = (1/2) ln (16 + u^2) + C

3 Answers · Science & Mathematics · 09/04/2011

8. ### Integral problem with u-substitution?

∫(u + 2)^2 * (u + 1)^(1/2) du from -1 to 0 Let z = u + 1 => dz = du ∫(z + 1)^2 * z^(1/2) dz from 0 to 1 (Note the ...

3 Answers · Science & Mathematics · 04/12/2013

9. ### 4u OVER u^2 PLUS u OVER u-1?

4u OVER u^2 PLUS u OVER u-1 = 4u/u^2 + u/(u - 1) = 4/u + u/(u - 1) = [4(u - 1) + 4u]/[u(u - 1)] = (8u - 4)/[u(u - 1)] = [4(2u - 1)]/[u(u - 1)] C over C^2 + 9c +20 MINUS...

1 Answers · Science & Mathematics · 25/10/2013

10. ### how to integrate 1/[ u*√(7-u^2)] du?

u = sqrt(7) * sin(t) du = sqrt(7) * cos(t) * dt du / (u * sqrt(7 - u^2)) => sqrt(7) * cos(t) * dt / (sqrt(7) * sin(t...sqrt(7)) * (ln|sin(t)| - ln|1 + sqrt(1 - sin(t)^2)| + C u = sqrt(7) * sin(t) u / sqrt(7) = sin(t) (1/sqrt(7)) * (ln|u...

3 Answers · Science & Mathematics · 01/05/2013