EXAMPLE 3 Find EXAMPLE 3 Find vom av 2 ox. SOLUTION Let u= 1 – 182. Then du = -88 I ho du SOLUTION Let u = 1 - 4x2. Then du = - 8x dx, so x dx = x, so x dx = -8 du and du and -1/2 du (2017) + c + C (in terms of x).
EXAMPLE 2 Find sin$(7x) cos”7x) dx. SOLUTION We could convert cos?(7x) to 1 - sin?(7x), but we would be left with an expression in terms of sin(7x) with no extra cos(7x) factor. Instead, we separate a single sine factor and rewrite the remaining sin" (7x) factor in terms of cos(7x): sin'(7x) cos”(7x) = (sinº(7x))2 cos(7x) sin(7x) = (1 - Cos?(7x))2 cos?(7x) sin(7x). in (7x) cos?(7x) and ich is which? Substituting u = cos(7x), we have du = -sin (3x) X...
Consider the second Galerkin Example (videos: GalerkinDiscrete-Example_1 to 3). Solve this example if u(0) = 0, du(2)/dx =0, and 0 ≤ x ≤2. Every single step must be shown. EXAMPLE Solve ODE using Galerkin method for two equal-length elements du u(0) = 0 +1 = 0, 0 < x < 1 dx2 du Boundary conditions (1) dx We know for three nodes: X2 = 0, X2=0.5, X3=1.0; displacement at nodes = Uy, U2, U3; length of elements L1=0.5, L2=0.5 -...
3. sin 7x dx du = Now rewrite the original integral in terms of u ONLY: Solve in terms of u: Substitute back. 4. Sx(ex) dx du Now rewrite the original integral in terms of u ONLY: Solve in terms of u: Substitute back.
By using u substitution Find fav? + 1dc by using substitution. 1. Let u= 2. Then du = 3. Solve for a from part "1". x2 = (Answer needs to be in terms of u and du. ) 5. integrate, leave in terms of u. 4. Make the substitution into the integral. po vo? + ide = f"x++ido I 6. Change your answer in 5 so that it is in terms of a 1dx =
U 12 1 . puy you tapi DU MIDU TOU DO 3. Let X have the pdf fx(x) = 33.52 Fr?e=22/B2, 0<I< for any B > 0. (a) Verify fx(x) is a pdf. (b) Find E(X) and Var(X). (c) Does My(t) exist? If so, find it.
Question Question 1 (1 mark) Attempt 1 Consider the boundary value problem: du+ U=1, 2<c<13 with u(2) = 4 and u(13) = 5 Find functions g and , such that u=gta, is a quadratic approximation that satisfies the boundary conditions. Your answer should consist of two expressions, the first representing the term g and the second representing the term ,. Both should be expressed in terms of the independent variable x. Your answers should be expressed as a function of...
is this correct? for: is this correct? for: 2 dx 19+x2 2 2 dac 2 х U 13 Z - dx = 3 Х + 3 21 3 34² +3 np 11 Surtide une Z arctan Surs de Su du Sax = 12 arctan 13 12 z arctan G) zt 13 .IT/Z x cos 2x dx cos 2x dx = x Cos (2x) Ste afg. Sto Fax.gi- cestzs) [" Sx cas 2x dx . X BN (2) -S SIN (2x)...
13. Find each of the following: 1 - dx 3 x 3 + + 3 a. х $x*(x° +1)* dx b. 2x 3e2 le dx C. e-* +5 4x3 - 1 dx d. 1 5 2x+1 x² + x-1 dx e.
2 points) Let H be the subspace of P2 spanned by 2x2 - 6x +3, x2 -2x 1 and -2r221 (a) A basis for H is Enter a polynomial or a list of polynomials separated by commas, in terms of lower-case x . For example x+1,x-2 (b) The dimension of H is c)Is (2x2 6x +3, x2 - 2x +1, -2x2 +2x 1 a basis for P2? 2 points) Let H be the subspace of P2 spanned by 2x2 -...