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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