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1. ### What is the integral of (u^2) (sqrt(u^2-1)) du?

u = sec(t) du = sec(t) * tan(t) * dt u^2 * sqrt(u^2 - 1) * du => sec(t)^2 * sqrt(sec(t)^2 - 1) * sec(t...sec(t) + (1/8) * sec(t) * tan(t) - (1/8) * ln|sec(t) + tan(t)| + C u = sec(t) u^2 = sec(t)^2 u^2 = 1 + tan(t)^2 u^2 - 1 = tan(t)^2 tan(t...

3 Answers · Science & Mathematics · 29/10/2013

2. ### How do you prove U+W is a subspace of V?

Since U and W are subspaces of V, all of their respective... under vector addition. Let x and y be elements of U + W. We can write, by definition, x = u_1 + w_1 and y = u_2 + w_2 (where...

3 Answers · Science & Mathematics · 18/02/2009

3. ### Can anyone help me with solving the following differential equation: u'' + ((2a)/t)u' + (b/t^2)u = 0?

u'' + (2a/t)u' + (b/t^2)u = 0 Let u = t^r ln(u) = rln(t) u'/u = r/t u' = ru/t u' = (r/t)t^r u '' = [t(d/dt(rt^r) - rt^r] / t^2 u '' = rt^r(r -1) / t...

1 Answers · Science & Mathematics · 15/06/2010

4. ### Consider the system of ODEs for u(x) and v(x)?

u' = u + v --> v = u' - u --> v' = u'' - u' v' = u'' - u' = -u + (u' - u) = sin(x) --> u'' - 2u' + 2u = sin(x) as noted above. I didn't put e^x as a factor because there...

2 Answers · Science & Mathematics · 22/10/2009

5. ### solve (u+6)^2 -64 = 0?

(u+6)² - 64 = 0 (u + 6)² = 64 (u + 6) = ± 8 u = 2, -14 Answer: u = 2 or u = -14

4 Answers · Science & Mathematics · 07/05/2011

6. ### use the dot product to find |u|?

| u | = sqrt(3^2 + (-4)^2) | u | = sqrt(9+16) |u| = sqrt(25) |u| = 5

2 Answers · Science & Mathematics · 07/12/2008

7. ### w = sinx + icosx and u = cscx + isecx ..?

|w| = sqrt( sin ^2 x + cos^2 x) = 1 |u]^2 = csc^2 x + sec^2 x = (1/ sin ^2 x) + (1/ cos^2 x) = ( cos^2 x + sin ^2 x)/ ( sin ^2 x cos ^2 x) = 1/ ( sin ^2 x cos^2 x) so |u| = 1/ ( sin x cos x) so |w/u] = |w|/|u| = sin x cos x

5 Answers · Science & Mathematics · 08/01/2012

8. ### Integration using substitution u = sec x?

Let u = sec(x) dx <==> du = sec(x)tan(x) dx. The integral ... now yields: ∫ sec^2(x) * [sec^2(x) - 1] [sec(x)tan(x) dx] = ∫ u^2*(u^2 - 1) du = ∫ (u^4 - u^2) du = (1/5)u^5 - (1/3)u^3 + C. ...

3 Answers · Science & Mathematics · 13/06/2010

9. ### U Substitution - Calculus One?

I'd integrate by parts ln(x)^2 * dx u = ln(x)^2 du = 2 * ln(x) * dx / x dv = dx v = x int(u * dv) = u * v - int(v * du...

2 Answers · Science & Mathematics · 09/05/2013

10. ### 10 points U substitution question?

u = sqrt(2x - 1) u^2 = 2x - 1 u^2 + 1 = 2x 2u * du = 2 * dx u * du = dx x * dx / sqrt(2x - 1) => (1/2) * (u^2 + 1) * u * du / u => (1/2) * (u^2 + 1) * du Integrate (1/2...

1 Answers · Science & Mathematics · 22/11/2015