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  1. Since u = x + 1, du = dx and x = u - 1. Bounds: If x = 0, then u = 0 + 1 = 1. If x = 1, then u = 1 + 1 = 2. Therefore, ∫(x = 0 to 1) x^2 √(x + 1) dx = ∫(u = 1 to...

    1 Answers · Science & Mathematics · 27/07/2010

  2. ∫ (x²)√(x + 1) dx = ? Let u = x + 1. Then: du/dx = 1 du = dx And (subtracting 1 from...)√(u) – 2u√(u) + √(u)] du = ∫ [u^(5/2) – 2u^(3/2) + u^(1/2)] du = (2/7)u^(7/2) – 2(2/5)u^(5/2) + (2/3)u^(3/2) + C = (2/7)u^(7/2) – (4/5)u...

    3 Answers · Science & Mathematics · 27/07/2010

  3. Let v be any vector in R^3 then for u=[-3,0,3]^T there exist a vector u_perp(v) such that: i.) v = a u + b u_perp...the solution. Take the dot product of (i) with respect to u: <u,v> = a <u,u> + b <u,u_perp> = a...

    2 Answers · Science & Mathematics · 11/04/2011

  4. ... "a" is a constant and the integral is taken from u=0 to u=a. (That is from x=a to x=0, but "x" is...

    2 Answers · Science & Mathematics · 29/06/2011

  5. You should know that U(28) is an abelian group of order phi(28), where phi is...there are any number of ways to see that U(28) is not cyclic. One is to compute the order...

    2 Answers · Science & Mathematics · 30/03/2012

  6. Let u(x, y) = X(x) Y(y). Substituting this into the ...for some C ==> Y = Ce^(25y^2/2). Therefore, u(x, y) = (A cos(5x) + B sin(5x)) * Ce^(25y^2/2...

    2 Answers · Science & Mathematics · 31/07/2015

  7. Rewrite this as dv/du = (2 + v/u)/(1 + 2v/u). Hence, this is a homogeneous DE. So, let v...we solve by separating variables: (1 + 2z) dz/(1 - z^2) = 2 du/u ==> (-1/2) (1/(z + 1) + 3/(z - 1)) dz = 2 du/u, by partial fractions ==>...

    1 Answers · Science & Mathematics · 20/09/2014

  8. U and V are vectors, U*T is the dot product...

    5 Answers · Science & Mathematics · 29/02/2008

  9. ...rewrite it as: ∫ sec²(e^x) e^x dx = let: e^x = u differentiate both sides: d(e^x) = du e^x dx = du...θ + 1)] sinθ cosθ dθ = let: (sin²θ + 1) = u differentiate both sides: d(sin²θ + 1) = du...

    1 Answers · Science & Mathematics · 24/01/2011

  10. first, let: u = 5x + 8 du = 5 dx (1/5) du = dx go ahead and make the first substitution, to get: ∫ (1/5) (15x + 4) / √(u) dx now, to get rid of the numerator, just take what u is equal to and solve for x 5x + 8 = u 5x + 8 - 8 = u - 8 5x = u - 8...

    2 Answers · Science & Mathematics · 12/12/2010

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