Use polar coordinates to evaluate || (2x-3y) dA, R ere R is the region in the upper half-plane bounded by the circles x²+y² = 4 and x²+y² = 9.

Q: Find the area of the region bounded above by the spiral r = π(3θ) and below by the polar axis,…

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Q: Sketch the indicated region D and integrate f(x, y) over D using polar coordinates. f(x, y) = 18xy,…

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Q: r2 0, Is es 2

A: We draw the graph of following function.

Q: Evaluate (x + 2y) dA, where R is the region bounded by the parabolas y = 2x² and y = 1 + r?.

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Q: Sketch the region in the plane consisting of points whose polar coordinates satisfy the given…

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Q: Consider the region R bounded by the parabolas y = and y = r - 3.r, as depicted in the graph below.

A: Since you have posted multiple questions but according to guidelines, we will solve the first…

Q: 2)use the polar coordinates to evaluate the double integral : A) || Vx2 + y² dA , R is the disk x² +…

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Q: Evaluate fS (3x + 4y²)dA by changing it into polar coordinates over the region in upper half plane…

A: In polar coordinates

Q: Using polar coordinates to evaluate (3x + 4y) dA, where R is the region in the upper half of the…

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Q: find the surface area of the portion of the surface z=4-x2/2 that lies above the region bounded by…

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Q: Find the centroid of the region in the polar coordinate plane defined by the inequalities 0<=…

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Q: Find a parametric representation for the part of the cylinder y2 + z² = 36 that lies between the…

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Q: 2. Evaluate f, z³ /x² + y² + z² dV where E is the solid hemisphere that lies above the xy-plane and…

A: Solution:- equation of sphere having centre origin (0,0) and radius=1 x2+y2+z2=1…

Q: OUTM a) Use polar coordinate to calculate dA, V3r where Ris the region bounded by y = I-7y = -r and…

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: Sketch the region in the plane consisting of points whose polar coordinates satisfy the given…

A: The region 3<r<4, 5π3≤θ≤7π3. We have to sketch this region.

Q: The base of a solid is the region in the xy-plane between the the lines y = x, y = 4x, x = 1 and x =…

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Q: 3. Use polar coordinates to find the surface area of the paraboloid z = x² +y² – 5 that lies below…

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Q: Find the area of the surface defined by z = xy and x2 + y2 < 7.

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Q: Find the area of the surface f(x,v)= 2 +12x + y over the domain bounded by the x-axis and the…

A: To find the area of a surface, do the following  Draw the region in a plane and shaded that region…

Q: lad Use Green's theorem to evaluate y² dx + 3xy dy, where c is the boundary of the semi annular…

A: Given Problem:- Use Green's theorem to evaluate ∮cy2dx+3xydy where c is the boundary of the semi…

Q: A. Find the area of the plane region bounded by the given curves 1. у%3Dх, у %3D 2х, and x + у %3D 6

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Q: Find the region in the xy-plane in which the following equation is hyperbolic: ((x- y)? - 1]u + 2u,…

A: Given partial differential equation x−y2−1uxx+2uxy+x−y2−1uyy=0 We have to find the region in the…

Q: Q4(a) Find the surface area of the part of the paraboloid z=10-x -y' that lies above the plane :=1.

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Q: Use polar coordinates to evaluate the double integral: /| 2yd A, where R is the region in the first…

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Q: The area of the surface obtained by rotating the curve y = -+ X°, 1sx< e about the line x = 24 is x3…

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Q: Find the area of the region enclosed by the parametric equation x = t3 – 8t y = 6t2

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Q: EX. Find the volune of the solid region lymg mside both the sphere Xtuf+2?= 402 and the cylmeder…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Use the transformation x = * and y = uv (with u > 0 and v > 0) to evaluate /| xy dA R where Ris the…

A: The integral is ∬Rxy2dA. Transformation: x=uv and y=uv We obtain the integral as follows:  ∬Rfx,…

Q: 1 x² dA, where R is the region enclosed by the circles x² + y² = 1 and x² + y² = e² + y² , by…

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Q: Evaluate the surface integral fF- dS where F = (52,-52, 5y) and S is the part of the sphere a² +2+22…

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Q: xy dA RVX² + y² a.) from Cartesian coordinates to polar coor- dinates where the region R is given on…

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Q: Use polar coordinates to evaluate the double integral. 1 1 + x² + y² where R is the sector in the…

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Q: Evaluate [F d$ for F = yi+=j+2xk and S is a surface of the region bounded by the cylinder x+ y = 4…

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Q: 2)use the polar coordinates to evaluate the double integral: )x2 +y2 dA R is the disk x2 + y2 < 9 A)

A: We have to use polar coordinates here.

Q: Find, by using polar coordinates in R2, the volume of the region bounded by the paraboloid z = 20 –…

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Q: Using polar coordinates, evaluate J*** dydr, R where R is the semicircular region bounded by the…

A: For a function f(x, y) In Polar coordinates x = r cos θ, y=r sin θ Find f(r, θ) Formula Used: ∫∫R…

Q: Find the area of the surface f(x,y)= x² + 3y over the triangular domain bounded by the x-axis, the…

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Q: 2)use the polar coordinates to evaluate the double integral A) | x2 + y2 dA , R is the disk x2 + y?…

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Q: Use polar coordinates to evaluate fy² dA, R where R is the region bounded by the line y = x, the…

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Q: Use polar coordinates to evaluate S (5x-y) dA gion in the fourth quadrant bounded by the circles nd…

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Q: se Stokes's Theorem to calculate (curl F) · n dS . 14) F = -2x2yi + 2xy²j + z°k; S is the portion of…

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Q: Let S be the solid obtained by rotating the region shown in the figure below about the y-axis. y…

A: The function of the curve is y = 6x(x-1)2.

Q: Evaluate y dx+3xy dy, where C is the boundary of the semiannual region D in the upper half-plane…

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Q: Evaluate the double integral Answer: dA, where R is the region that lies between the circles x² + y²…

A: Explanation of the answer is as follows

Q: Find the surface area of that portion of the surface Z = 4 -x that lies above the rectangle R in the…

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Q: Find the area of the part of the plane 5x + 4y + z = 20 that lies in the first octant. (Use…

A: Part of the plane equation   5x+4y+z=20⇒z=20-5x-4yPlane lies in the first octant , so x≥0 ,…

Q: c) By using Green's theorem, evaluate (In (z²) + ry? – y²) dr + (c" + r*y-3ry) dy, where C is the…

A: We have to evaluate ∮Clnx2+xy2-y2dx+ey+x2y-3xydy where C is the region bounded by the circles…

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

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