pts.) Verify Green's Theorem by evaluating BOTH sides of the equation to show that they are l: Cy2dy +X2dymar-a(pa fortepathgivenbyC: boundaryoftheregionlyingbetw the graphs of y xand y x. Ex...
-/1.42 POINTS LARCALC10 15.4.003. Verify Green's Theorem by evaluating both integrals [x?dx + x? dy = f S (x om) da for the given path. C: square with vertices (0,0), (3, 0), (3, 3), (0, 3) { y dx + x² dy =
1. [-/10 Points] DETAILS LARCALC11 15.4.005. 0/6 Submissions Used Verify Green's Theorem by evaluating both integrals Ja yax+ y2 dx + x2 dy дм ду for the given path. C: boundary of the region lying between the graphs of y = x and y = x2 + x2 dy AS COMO an дх aM ду dA =
Stokes' Theorem Verify Stokes' Theorem by evaluating each side of the equation in the theorem Here, F (x2 y, y2 - z2,z2 -x2) S is the plane x + y z 1 in the first octant, oriented with upward pointing normal vector, and y is the boundary of S oriented counterclockwise when seen from above. State Stokes' Theorem in its entirety Sketch the surface S and curve, y Explain in detail how all the conditions of the hypothesis of the...
Gauss's Divergence Theorem Verify Gauss's Divergence Theorem by evaluating each side of the equation in the theorem. Here, Here, \(\vec{F}=y \vec{\imath}-x \vec{\jmath}\), and \(S\) is the hemisphere \(x^{2}+y^{2}+z^{2}=9, z \geq 0\), with boundary \(\gamma: x^{2}+y^{2}=9, z=0\)State the Divergence Theorem in its entirety. Sketch the surface S and curve, γExplain in detail how all the conditions of the hypothesis of the theorem are satisfied Show all work using proper notation throughout your solutions. Simplify your answers completely
2. [-/10 Points] DETAILS LARCALC11 15.4.007. 0/6 Submission Verify Green's Theorem by evaluating both integrals |_ ? dx + x? dy = f S (mmen med dA for the given path. C: square with vertices (0,0), (2, 0), (2, 2), (0, 2) Je v2 dx + x² ay = an ax дм ay dA Need Help? Read It Talk to a Tutor
CAS 15-16 Verify Green's Theorem by using a computer algebra system to evaluate both the line integral and the double integral. 15. P(x, y) = x’yt, Q(x, y) = x®y4, C consists of the line segment from (- /2, 0) to (TT/2, 0) followed by the arc of the curve y = cos x from (TT/2, 0) to (- 2, 0)
13. (6 pts) FTLIs, Green's, and Divergence Theorems (a) Complete the table below. Theorem Need to check: FTLIs The vector field Il curve Il surface IS: Green's Theorem | The vector field II curve ll surface is: and: Divergence Theorem The vector field |l curve l surface is: (b) For each of the following, choose all correct answers from the list below that can be used to evaluate the given integral. List items may be used more than once. i....
Evaluating using Green's theorem (4x^3+sin(y^2))dy-(4y^3+cos(x^2))dx where C is the boundary of the region x^2+y^24 Please be detail thanks. We were unable to transcribe this image3. EVALUATE USING GREEN'S THEOREM (4x++sinyydy –(4y+cosx2) dx, WHERE C IS THE BOUNDARY OF THE REGION X+Y24.
7.) (12 pts.) Verify Green's Theroem 2 for the Vector Field F(x, y) = (xy)i + (y?)3, where the closed curve C is the circle x² + y2 = 1.
3. Use the curl test to show that F(x,y)- (x2yi+(y)j is path dependent. 4. Use Green's Theorem to evaluate the line integral , (2x-y)dx-r3)dy where C is the boundary of the region between y = 2x and y-x2 oriented in the positive direction 3. Use the curl test to show that F(x,y)- (x2yi+(y)j is path dependent. 4. Use Green's Theorem to evaluate the line integral , (2x-y)dx-r3)dy where C is the boundary of the region between y = 2x and...