Consider the transformation x = p sin o cos 0, y = p sin o sin 0, z= p cos o from spherical to rectangular coordinates, where 0 <¢< T. Find a (x, y, z) a (p, ¢, 0)

Q: /| 2rdV, where E is the region under the plane 2r + 3y + z = 6 that lies in the first octant as…

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Q: Y – 5x |dA 100 cos x + y

A: We have to evaluate the double integral ∬100cosy-5xx+ydxdy over the region D where the region D is a…

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

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Q: Change the Cartesian integral into an equivalent polar integral. 2 2 a -x 00 S SO dy dx = dr de 2 2…

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Q: Use Green's Theorem to evaluate the line integral v+e*) dx + (6x+cosy) dy where C is the triangle…

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Q: Sketch the indicated region D and integrate f(x, y) over D using polar coordinates. = V x2 + y2, D:…

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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: Compute the Jacobian for the change of variables into spherical coordinates: x = p sin o cos 0, y =…

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Q: Find the decomposition of a(t) a = arT + anN into tangential and normal components for r(t) =…

A: Given

Q: Question 3. Compute the integral dz 8+z where y is the rectangle with vertices +3+i with the…

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Q: Graphic r+y = 1 R Options f(r cos(8), T sen(0)) /2 A) I = drd0 1-r cos(0) /2 B) I = f(r cos(0), r…

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Q: can u help me with this Jacobian question please

A: Given transformation is

Q: Consider the transformation x=r cos θ, y=r sin θ, z=z from cylindrical to rectangular coordinates…

A: Given; x = r cos(theta), y = r sin(theta), z=z.

Q: Change to polar integral e-(z²+y*) dydx -1 1 -y1-z² o s: So re *drde drde re o f re *drde drde

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Q: Change the Cartesian integral to an equivalent polar integral VI-x² e-(x²+y²) dy dx O re-r re dr dt…

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Q: Compute the line integral of i = (p cos? 0)p - (p cos 0 sin 0)0 + 3po, around the path shown in the…

A: We need to find line integral.

Q: Evaluate the line integral g. xy? dx + 2x²y dy, where C is the triangle with vertices (0,0), (2, 2),…

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Q: Evaluate cos z dz , where C is the circle |z – 1| = 3. (Integrate counterclockwise around C.)

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Q: (c) Use Green's Theorem to evaluate 3xy dx + 2xy dy, where C is a counterclockwise oriented…

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Q: 1. Find the moment of inertial of the rectangular area of Figure 1.0 about the centroidal x and y…

A: we only solve one problem at a time so please submit them one by one.

Q: 3. Sketch the image of the sector {0 < arg z < T/6} under the map w = , (b) a = za for (a) a = i,…

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Q: 10. Use polar coordinates to evaluate the integral 2-³ drdy D = {(r,y) E R°lx² + y² > 9}

A: Hello, thanks for your question but as per our policy we can not provide hand written solution.…

Q: Y – 5x |dA x + y 100 cos

A: We have to evaluate the double integral ∬ 100cosy-5xx+ydxdy over the region D where D is the…

Q: Convert the integral | dy dx to polar coordinates and evaluate it (use t for 0): With a = , b = ,c =…

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Q: By converting to polar form, integrate the In(x? + y?) x2 + y? function f(x, y) over the region 1…

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Q: Evaluate the line integral (cos x + sin y) ds; C is the line segment from (0, 0) to (x, 67).

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

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Q: Calculate the circulation of A = p cos ap + z sin o az around the edge L of the wedge defined by 0 ≤…

A: Yes , we can solve using stokes theorem. Note that all the cases z = 0

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

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

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Q: Evaluate the triple integral [ 2³ dV, where E is the solid tetrahedron with vertices (0,0,0),…

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Q: 1. Convert the integral in polar coordinates: 8e-2-y? I F(r, 0) dr de е dy dæ a = [ Select ] b = […

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Q: Use Green's Theorem to evaluate the line integral.       Cy dx + 7x dy C: square with vertices (0,…

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Q: 1. Determine the centroid of the first full enclosed region in the first quadrant between sin r and…

A: given curves are                                              f(x)=sinxg(x)=cosx graph of the…

Q: Use either form of Green's Theorem to evaluate the following line integral. 03x y dx+ 4x y dy; C is…

A: According to the given information, it is required to find the value of integral using Green’s…

Q: Let R be the region enclosed by the polar curve r (0) = 3 ln (0) where 7π <O< 8 Y X 72 ㅠ R 1 1

A: Given Curve rθ=3ln(θ)whereπ2≤θ≤7π8

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

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Q: 3) Let : R2 -R given by (r, 0) = (r cos(@), r sin(0)), 0 Srs R, 0 <0S 27 (this is a disk of radius R…

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Q: When transforming the triple integral 9-x2 9-x2-y2 (x²+ y² + z²)% dzdydx 2n n 3 to spherical…

A: The formula for the conversion of triple cartesian to triple polar coordinate is…

Q: Let R be the region inside the ellipse x = 4 cos 0, y = 3 sin and outside the circle x = 2 cos 0, y…

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Q: Consider the transformation x = r cos Oy =r sin = zfrom cylinderical to rectangular coordinates,…

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Q: Use Green's Theorem to evaluate x' dx + xy dy where C is the triangle with vertices (0,0), (1,4),…

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

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

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

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

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Q: The image of the rectangle S = {(r, 0): 1<r< 2,0<0S a/2} under the transformation T: x = r cos 0, y…

A: The given rectangle S=r,θ:1≤r≤2, 0≤θ≤π2 under the transformation T: x=r cosθ, y=r sinθ. Draw the…

Q: Consider the transformation a = p sin p cos 0, y = p sin ø sin 0, z = p cos ¢ from spherical to…

A: Given that: x=ρsinϕcosθy=ρsinϕsinθz=ρcosϕ