Evaluate ∫y0ksin(kx−π)dx where y and k are independent of x, and y is given by the solution to the equation cos(ky)=0.68 .

Evaluate ∫y0ksin(kx−π)dx where y and k are independent of x, and y is given by the...
Evaluate the integral Z π 0 Z π x cos(y) y dy dx. Hint: Since cos(y) y doesn’t have an elementary antiderivative in y, the integral can only be evaluated by reversing the order of integration using Fubini’s theorem.
Show that sin (kx) and cos (kx) given in Eq. (11-48a) are two independent solutions of the differentia equation, Eq. (11-47a). Consider a rectangular wavequide haing dimoneinc 404 We were unable to transcribe this image(11-48a) X(x)- Asin(k,x)+B cos (k,x)
If a quantity y satisfies the differential equation dy = kx(10-y), k>0 dx. when X = 2 and y = -7, the graph of yir increasing decreasing constant cannot be determined
dy Find the solution of differential equation: - cot(y). (KER) dx y=K sin(e) y=arcsin(Ket) O y=tan(Kx?) y=Ke* y = arccos(Ke-*) y=sin(e" +K) O
Consider the following wave function: y(x, t) = cos(kx - omega t). a. Show that the above function is an eigenfunction of the operator partialdifferential^2/partialdifferential x^2[...] and determine its eigenvalue. b. Show that the above function is a solution of the wave equation expressed as partialdifferential^2 y(x, t)/partialdifferential x^2 = 1/v^2 partialdifferential^2 y(x, t)/partialdifferential t^2, given the wave velocity is v = omega/k (where omega = 2 pi V and k = 2pi/lambda).
Solution and work
(35 p) Evaluate the line integralſ, ex cos y dx + (ey – ex sin y) dy where C is the semicircle given by the following parametric representation: x – 1 = cost, y - 1 = sint, 0 <t <n.
Use Green's Theorem to evaluate the line integral sin x cos y dx + xy + cos a sin y) dy where is the boundary of the region lying between the graphs of y = x and y = 22.
7. Given the joint density function /(x,y) =(kx (1 + 3 y*) 0<x<2,0<p?1 elsewhere a. Find k, g() h) and f(x) b. Evaluate P(-<X<1)
Use Green's Theorem to evaluate the line integral dos sin x cos y dx + xy + cos x sin y) dy where is the boundary of the region lying between the graphs of y = x and y = 22.
Use Green's Theorem to evaluate the line integral fo sin x cos y dx + (xy + cos x sin y) dy where is the boundary of the region lying between the graphs of y = x and y= 22.