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1. ### Evaluate using u-substitution?

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. ### Evaluate using u-substitution?

∫ (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. ### Find the length of the projection of the vector u = [-3, 0, 3]^T on the vector v= [ 0, 0, -3]^T?

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. ### please could anyone explain this step ∫1/(2a)√(u) du = a²/3.?

... "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. ### Use the Fundamental Theorem of Finite Abelian Groups to conclude that U(28) ∼= Z2 ⊕ Z2 ⊕ Z3 .?

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. ### Use separation of variables with λ = 25 to find a product solution to the following partial differential equation, y(∂^2u/∂x^2) +(∂u/∂y)= 0?

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. ### Solve the homogeneous equation dv/du=(2u+v)/(u+2v).?

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. ### Why is the product of vectors u X (v • w) meaningless?

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

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

9. ### How do you integrate using u-substitution?

...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. ### The substitution u=5x+8 transforms the "x"-integral...?

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