Homework Statement
Use, using the result that for a simple closed curve C in the plane the area enclosed is:
A = (1/2)∫(x dy - y dx) to find the area inside the curve x^(2/3) + y^(2/3) = 4
Homework Equations
Green's Theorem:
∫P dx + Q dy = ∫∫ dQ/dx - dP/dy
The Attempt at a Solution
I...
Homework Statement
Use Green's Theorum to evaluate the line integral ∫c (x^2)y dx, where c is the unit circle centered at the origin.
Homework EquationsThe Attempt at a Solution
Taking the partial derivative with respect to y and subtracting it from zero(I'm taking the dy in the original...
Homework Statement
Evaluate ∫∫∫[W] xz dV, where W is the domain bounded by the elliptic cylinder (x^2)/4 + (y^2)/9 = 1 and the sphere x^2 + y^2 + z^2 = 16 in the first octant x> or = 0, y> or = 0, z> or = 0.
Homework Equations
First, I tried to find the bounds for z:
z = 0 (because z is...
Homework Statement
The distance between the first and fifth minima of a single-slit diffraction pattern is 0.350 mm with the screen 45.0 cm away from the slit, when light of wavelength 550 nm is used. (a) Find the slit width. (b) Calculate the angle θ of the first diffraction minimum...
Homework Statement
Figure 29-61 shows a cross section of a long thin ribbon of width w = 4.91 cm that is carrying a uniformly distributed total current i = 4.61 * 10^-6 A into the page. What is the magnetic field at a point in the plane of the ribbon at a distance 2.16 cm from its edge...
A block attached to a spring (which is attached to a wall) lies on a horizontal frictionless surface, and the spring constant is 50 N/m. Initially, the spring is at its relaxed length and the block is stationary at position x = 0. Then an applied force with a constant magnitude of 3.0 N pulls...