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What does 1 W on a U mean?
1 wheel on a unicycle
1 equals W on a U?
1 wheel on a unicycle
Alphabet letters with symmetry?
Lowercase letters would be; c, l, o, v,w, x, and sometimes m,n, t and u. Uppercase are A, B, C, D, E, H, I, K, M, O, T, U, V, W, X, and Y.
Integration cos3 x?
Take f(x) = cos(3x) ∫ f(x) dx = ∫ cos(3x) dx Take u=3x → du = 3dx = ∫ 1/3*cos(u) du = 1/3*∫ cos(u) du = 1/3*sin(u) + C, C ∈ ℝ = 1/3*sin(3x) + C
What is the indefinite integral of 2x ln2x dx?
In order to work out this problem, we need to learn how to apply the integration method correctly.The given expression is ∫ 2xln(2x) dx.Instead of working out with 2x's, we let u = 2x. Then, du = 2 dx or du/2 = dx. This method is both valid and easy to avoid working out with too much expressions. You should get:∫ uln(u) (du/2)= ½ ∫ uln(u) duUse integration by parts, which states that:∫ f(dg) = fg - ∫ g(df)We let:f = ln(u). Then, df = 1/u dudg = u du. Then, g = ∫ u du = ½u²Using these substitutions, we now have:½(½u²ln(u) - ½∫ u du)= ¼(u²ln(u) - ∫ u du)Finally, by integration, we obtain:¼ * (u²ln(u) - ½u²) + c= 1/8 * (2u²ln(u) - u²) + c= 1/8 * (2(2x)²ln(u) - (2x)²) + c= 1/8 * (2x)² * (2ln(u) - 1) + c= ½ * x² * (2ln(2x - 1)) + c
