Question

In: Advanced Math

Verify the green theorem for: P (x, y) = 2xy Q (x, y) = x +...

Verify the green theorem for:
P (x, y) = 2xy
Q (x, y) = x + y
C is the curve formed by the line segments from (0,0) to (3,0), from (3,0) to (2,1) and from (2,1) to (0,0)


For the line integral, you can solve through the parameterization analysis please

Solutions

Expert Solution


Related Solutions

Verify the Divergence Theorem for the vector field F(x, y, z) = < y, x ,...
Verify the Divergence Theorem for the vector field F(x, y, z) = < y, x , z^2 > on the region E bounded by the planes y + z = 2, z = 0 and the cylinder x^2 + y^2 = 1. By Surface Integral: By Triple Integral:
Verify the Divergence Theorem for the vector eld F(x; y; z) = hy; x; z2i on...
Verify the Divergence Theorem for the vector eld F(x; y; z) = hy; x; z2i on the region E bounded by the planes y + z = 2, z = 0 and the cylinder x2 + y2 = 1. Surface Integral: Triple Integral:
Consider the homogeneous second order equation y′′+p(x)y′+q(x)y=0. Using the Wronskian, find functions p(x) and q(x) such...
Consider the homogeneous second order equation y′′+p(x)y′+q(x)y=0. Using the Wronskian, find functions p(x) and q(x) such that the differential equation has solutions sinx and 1+cosx. Finally, find a homogeneous third order differential equation with constant coefficients where sinx and 1+cosx are solutions.
Verify Stokes theorem for F =(y^2 + x^2 - x^2)i + (z^2 + x^2 - y^2)j...
Verify Stokes theorem for F =(y^2 + x^2 - x^2)i + (z^2 + x^2 - y^2)j + (x^2 + y^2 - z^2)k over the portion of the surface x^2 + y^2 -2ax + az = 0
Given the function u(p,q,r)=((p-q)/(q-r)), with p=x+y+z,q=x-y+z, and r=x+y-z, find the partial derivatives au/ax=, au/ay=, au/az=
Given the function u(p,q,r)=((p-q)/(q-r)), with p=x+y+z,q=x-y+z, and r=x+y-z, find the partial derivatives au/ax=, au/ay=, au/az=
(Theorem 3.1): If xp is any solution of (∗) x′′ + p(t)x′ + q(t)x = f...
(Theorem 3.1): If xp is any solution of (∗) x′′ + p(t)x′ + q(t)x = f (t), and xh is a general solution of (∗∗) x′′ + p(t)x′ + q(t)x = 0), then the sum x = xh + xp is a general solution of (∗). (a) First show that x = xp + xh satisfies (∗). (b) Next show that if xp1 and xp2 are any two solution of (∗) then x = xp1 − xp2 satisfies (∗∗). (c)...
Prove that P1, P2 ⊢ C P1: (∀x)(∃y)(P(x) ⇒ (Q(y) ∧ T(x, y)∧ ∼ S(x, y)))...
Prove that P1, P2 ⊢ C P1: (∀x)(∃y)(P(x) ⇒ (Q(y) ∧ T(x, y)∧ ∼ S(x, y))) P2: (∃x)(∀y)(P(x) ∧ ((Q(y) ∧ R(x, y)) ⇒ S(x, y))) C: ∼ (∀x)(∀y)((P(x) ⇒∼ T(x, y)) ∨ (Q(y) ⇒ R(x, y)))
P = 2xy + ? 2 + ??, ? = 2xy + ? 2 + ??,...
P = 2xy + ? 2 + ??, ? = 2xy + ? 2 + ??, ? = ?? olacak şekilde bir vektör alanı veriliyor. A (1,2,3) ve B (2,1,5) olmak üzere şayet varsa verilen vektör alanının potansiyel fonksiyonunu bulunuz. Bu vektör alanında ∫ ??? ? ? + ??? + ??? eğrisel integralinin değerini hesaplayınız. find a potential function and calculate the integral
5. Equations of the form y’ = P(x)*y^2 + Q(x)*y + R(x) are called Riccati equations....
5. Equations of the form y’ = P(x)*y^2 + Q(x)*y + R(x) are called Riccati equations. i) If we know a solution y = φ(x) of this equation, then any other solution can be written in the form y(x) = φ(x)+ 1/v(x), where v(x) is an unknown function which satisfies a certain linear equation. Using the fact that φ and y both solve the above Riccati equation, find the differential equation that v satisfies. ii) Consider the equation 3y’ +...
5. Equations of the form y’ = P(x)*y^2 + Q(x)*y + R(x) are called Riccati equations....
5. Equations of the form y’ = P(x)*y^2 + Q(x)*y + R(x) are called Riccati equations. i) If we know a solution y = φ(x) of this equation, then any other solution can be written in the form y(x) = φ(x)+ 1/v(x), where v(x) is an unknown function which satisfies a certain linear equation. Using the fact that φ and y both solve the above Riccati equation, find the differential equation that v satisfies. ii) Consider the equation 3y’ +...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT