Consider the transformation x = r cos Oy =r sin = zfrom cylinderical to rectangular coordinates, a(z, y, 2) a(r, 8, z) ' where r > OFind -1

Q: Consider the transformation x = r cos Q y = r sin Pz = zfrom cylinderical to rectangular…

A:

Q: Find the Jacobian ∂(x, y)/∂(u, y) of the transformation x = u cos v v = u sin v

A:

Q: 4. Calculate the integral (x – 3y) dA where R is the triangular region with vertices (0,0), (2, 1)…

A:

Q: sin y dV, where E lies below the plane z = x and above the triangular region with vertices (0, 0,…

A: Given, the region E lies below the plane z = x and above the triangular region with vertices 0,0,0,…

Q: 2) Show that the integral f. (cosyz dx – xz sinyz dy – xy sinyz dz) is path independent and find its…

A:

Q: 6. Do the following tasks using Mathematica. // sin(9x2 + 4y²)dA , where R is the region in the…

A:

Q: Consider the transformation x = p sin o cos 0, y = p sin o sin 0, z= p cos o from spherical to…

A:

Q: 1. Compute the line integral (circulation in this case) of F(x, y) around the unit circle C starting…

A:

Q: Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise. 2x + 3y dx + e…

A:

Q: 18. Show that the centroid of the sector in Figure 13 has y-coordinate 2R sin o (0, y) R FIGURE 13

A:

Q: Find the Jacobian for the transformation x = 3u + v and y = u+ 3v. NEXT, use this transformation to…

A:

Q: G: Evaluate 4 px=(y/2)+1 2х - у Z. dx dy dz 3 0 Jx=y/2 by applying the transformation u = и %3D (2х…

A: Given the integral  We need to applying the transformation, u = (2x-y)/2 ,  v = y/2  and  w = z/3…

Q: 3. Use Stokes' Theorem to evaluate $ F dr, where F = (0, 0, 2), (1, 0, 2), (1, 1, 2), and (0, 1, 2),…

A:

Q: 1. Use an appropriate transformation of coordinates to evaluate xy dA where the region D is enclosed…

A: Special transformation is used to calculate double integral. Given integral is enclosed with the…

Q: Evaluate the triple integral∭E xy dV where E is the solid tetrahedon with vertices…

A: Given Data : Triple Integral ∬∫ExydV and E is the solid tetrahedron with vertices 0,0,0,…

Q: 10. a. Find the Jacobian of the transformation x = u, y = uv and sketch the region G: 1 < u < 2, 1 <…

A:

Q: Sketch the image S in the uv-plane of the region R in the xy-plane using the given transformation. x…

A:

Q: Use the given transformation to evaluate the integral, 3 cos(5((y-x)/(y+x))) dA u = y − x, v = y + x…

A: Given that the integral,

Q: Evaluate the integral 1 2x – y dīdy 2 by applying the transformation 21 – y and 2 y 2 and…

A: Given integral is ∫04∫y2y2+12x-y2dxdy In region R where y2≤x≤y2+1 and 0≤y≤4 Given transformation T…

Q: Use the transformation u = y - x, v = y, to evaluate the integral on the parallelogram R of vertices…

A:

Q: Consider the transformation æ = r cos 0, y=r sin 0, z= z from cylinderical to rectangular…

A:

Q: Find the coordinates of the centroid of the curve x = cos t + t sin t, y = sin t - t cos t, 0 … t ……

A: coordinates of the centroid of the curve  x=cost+tsinty=sint-tcost…

Q: 10. a. Find the Jacobian of the transformation x = u, y sketch the region G: 1 < u < 2, 1 < uv < 2,…

A: Given: x=u,y=uv.Interval 1≤u≤2 and  1≤uv≤2

Q: (a) Find the line integral of f (x, y, z) = -x + y + z over the straight-line %3D segment from (1,…

A:

Q: Use the transformation u = y - x, v = y, to evaluate the integrals on the parallelogram R which has…

A: We need to evaluate the integral: ∬Ry-xdA using the transformations: u=y-x, v=y. Here, R is a…

Q: Find the Jacobian for the transformation x 3u cos v and y = 4u sin v. %3D NEXT, use this…

A: Given, x=3u cosvy=4u sinv

Q: Use the Laplace transformation to solve the problem: x > 0, t>0 u(0,t) = 3t + 8 sinh 4t, lim u(x, t)…

A:

Q: Use the Laplace transformation to solve the problem: o'u o'u x>0, t>0 %3D u(0,t) 4t+10 sinh 1t, lim…

A:

Q: Find the Jacobian d(x,y,z)/ d(u,v,w) of the transformations below. a. x = u cos v, y = 4u sin v, z…

A:

Q: Solve by Laplace transform Utt – 9urz = 0, 0 0 %3D u(0, t) = u(r, t) = 0, %| %3D u (x, 0) = 0,…

A:

Q: Evaluate the integral |(x-y)dA; where D is the region inside the trapezoidal bounded by the points…

A: we will find region of integral for new variable to find  range of integral and then use jacobian to…

Q: 16. Use the transformation x = u – v², y = 2uv to evaluate the integral r2Vī-x Vx² + y² dy dx.…

A:

Q: Given the joint PDF of X and Y: f(x, y) = e-(*+y), x> 0, y> 0; 0 otherwise. Let U V = X + Y. Using…

A:

Q: Consider the transformation x = p sin o cos 0, y= p sin o sin 0, z = p cos o from spherical to…

A:

Q: Evaluate the line integral | F•ds where F = 2xyi +(x – y²)j and C is (a) y=x from (0,0) to (1,1) (b)…

A:

Q: Evaluate the iterated integral LL V-6x-x2 ху (x2 + y2)3/2 dydx -3 J0 using polar coordinates.

A:

Q: Let D be the solid region in the first octant bonded above by z-3 and below by 2= 2++y. Then the…

A: Here we will have to project the 3-dimensional solid regions on a 2-dimensional plane. Hence, we…

Q: z-1 -, find the image of the circle (i) z|=1 inthe w - plane. 1-iz Under the transform ati on w =

A:

Q: Use Green's theorem to calculate the integral -dx + dy, where C is a rectangle with vertices (–1,1),…

A:

Q: Find the Jacobian for the transformation x = 3u + v and yY= u+3v. NEXT, use this transformation to…

A: We have given transformation x=3u+v and y=u+3v Jacobian J=dxdudxdvdydudydv

Q: What is the Jacobian of the transformation T that arises from an appropriate change of variables to…

A:

Q: Use Green's Theorem to evaluate the line integral. Orient the curve counterclockwise. e5x + 2y dx +…

A:

Q: Let E be the solid hemisphere x2 + y2 + z2 < 4 with Consider the spherical coordinates…

A:

Q: Evaluate the line integral [F-dš where F = 2xyi + (x – y')j and C is (a) y =x from (0,0) to %3D…

A: For the solution follow the next steps.

Q: Sketch the image S in the uv-plane of the region R in the xy-plane using the given transformations 1…

A:

Q: Find the coordinates of the centroid of the curve x = cos t + t sin t, y = sin t - t cos t, 0…

A: Given,

Q: Find the divergence and curl of F = (e¬* sin y , e¯Y sin z , e-² sin x). %3D

A:

Q: Consider the transformation =r cos 0, y =r sin 0, z = zfrom cylinderical to rectangular coordinates,…

A:

Q: EXAMPLE 4 Line integral as a double integral Evaluate (4x³ + sin y²) dy – (4y³ + cos x²) dx, where C…

A: