4. Calculate the transition moment integral <2|-(Ēūl> for y-polarized light.
3. Calculate F. dr for F(x, y) =<x,y> using only one integral where is the path shown below. 4 -3 -2 -1 2 3
Given a polarized sphere with and electric field
Determine potential and electrostatic energy.
Can you do the potential using the line integral of the electric
field. i have some doubts how to do the math.
PT) = Art moglo E() = Ar --fir < R Eo or > R
Determine the moment of inertia of the shaded area about the x
axis and the y axis.
Figure < 1 of 1 > 1 m
1. Let F(x,y,z) =< 32, 5x, – 2y >. Use Stokes's Theorem to evaluate the integral Scurl F.ds, where S is the part of the paraboloid z = x² + y2 that lies below the plane z = 4 with upward- pointing normal vector.
Could someone explain how these to get these phase portraits by
hand with ẋ=y and ẏ=ax-x^2 especially for a=0 case where you have
eigenvalues all equal to zero?
6.5.4 a>0 Sketch the phase portrait for the system x = ax-x, for a < 0, a = 0, and For a -(0 We were unable to transcribe this imageFor a>0 ES CS
With double integral find surface area when y=e", y = x, y = 4 and axis y with y <et
Write the parametric equations
x=2siny=4cos0
in the given Cartesian form.
y^2/16= with x0.
Write the parametric equations
x=2sin2y=5cos2
in the given Catesian form.
y= with 0x2.
Write the parametric equations
x=4ety=8e−t
as a function of x in Cartesian form.
y= with x0.
Write the parametric equations x = 2 sin 0, y = 4 cos 0, 0<O< in the given Cartesian form. = with x > 0. 16 Write the parametric equations x = 2 sin’e, y = 5 cos?...
differential equations
Problem 2 Solve y"+y= ſt/2, if 0 <t<6, if t > 6 y(0) = 6, 7(0) = 8
17.3 Evaluate the following integral: SSR cosh(x + y)dA where R is the region bounded by x > 0, y = 0 and the line x + 2y = 2.
step by step please, thank
you
(2) Use Stokes' Theorem to evaluate the integral F.dr, where F(x, y, z) =< -Y, I, z > and where S is the upper hemispherical surface defined by z = v1- 2 - y2. The boundary of S is the curve C defined by Cos (t) y= sin (t) 0t 27 Z=0