1. Find Sp(r+2y)dA, where D is the region bounded by the parabolas y = r2, and y=1+2

Q: (b) / = xyz dV if S is the region bounded by the cylinders x² + y² = 25, x² + z² = 25 and the first…

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Q: (d) |// Vx² + y² dV, where P is the region under the cone z = 2 – ry-plane. /x² + y² and above the…

A: Since you have asked for a multiple question, we will solve the first question for you. If you want…

Q: x² sin xy 14.5.8. || - dA(x, y), if D is the region bounded by æ² = "4, x² = TY, y² = ;, and D y? =…

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Q: S.(2x° +5y )dx+(2x-4y') dy C:boundary of the region lying between the graphs of x² +y² = 16 and x +y…

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Q: 10. (1 – y³) dx + (x³ + e*) dy, Č is the boundary of the region between the circles x² + y² = 4 and…

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Q: The area of the region bounded by the curves 2y2 +2 and z 2y+2 is 2. 3 5 -1 -2 16 17 (A) 3 (B) 3 13…

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Q: 2. Evaluate f (3x + 4y2) dA, where R is the region in the upper half-plane 15 bounded by the circles…

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Q: 1. Compute  E yz dV , where E is the region above z  0, below z  y, and inside x 2 y 2  4

A: Obtain the limit of integration as follows.

Q: |(x+2y)d4, where D is the region bounded by the parabolas y=2x² D and y =1+x.

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Q: EXAMPLE 2 to evaluate the Use the change of variables x = u² - v², y = auv integral SSR y dA, where…

A: The objective is to evaluate the integral using change of variable. x=u2-v2, y=2uvy2=4-4x, y2=4+4x,…

Q: Calculate the double integral Sle (x² + 2y) dA, where R is the triangular region with vertices 8/3…

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Q: .Find the exact value of the double integral. J (2x + 5y) dA, where R is the rectangular region…

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Q: Volumes of solids Find the volume of the following solids.

A: The region is bounded by the curves, The region is shown in the graph given below,

Q: Evaluate |[(x+2y)dA,where D is the region bounded by the parabolas y= 2x D and y=1+x².

A: We can help you with the question. I am not sure how to help you with its attachments.

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

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Q: 17. Find the exact area of the surface z = 1 + 2x + 3y + 4y2, 1x 4, 0 y < 1

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Q: (b) ||| ryz dV if S is the region bounded above by x² + y² + z² = 16 and below the cone z = Vr2 + y²…

A: In cylindrical coordinates,                                                               and…

Q: /| (x + 2y)dA D.

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Q: 3. Let R be the region below bounded by the parabola y = 4x² and the lines 3x - 2y +3=0 and y = = 0.…

A: Follow the procedure given below.

Q: 3. Use Green's Theorem to evaluate (e3x +y²)dx + (sin y – x²)dy where C is the boundary of the…

A: Green's theorem

Q: Evaluate SS x² y4 dx dy D 1 where D is the region bounded by the hyperbolas xy-2, xyalk parabolas y²…

A: We have to Evaluate the integral  ∬Dx2y-4dxdy where D is the region bounded by the hyperbolas xy=2,…

Q: (1- y*)dx + (x° + e*)dy where C is the boundary of the region between the circles x² + y² = 4 and x²…

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

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Q: 4. Evaluate fe cosy dx + (xy – xsiny) dy where C is the boundary of the region lying between the…

A: Given  ∫Ccosydx+(xy-xsiny)dy

Q: 1. Compute fSSp(z+1)°dV where E is the region lying inside the sphere x² +y² + 22 = 1 of radius 1…

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Q: Given (1 + y³)y' = x². (i) Determine a region of the xy-plane for which the given differentia…

A: Explanation of the solution is given below...

Q: Evaluate ∫∫∫E √x2 + z2dV, where E is the region bounded by the paraboloid y = x2 + z2 and the plane…

A: Given, y=x2+z2 ⇒z2=y-x2z=±y-x2 Therefore the limit of z is -y-x2≤z≤y-x2 On drawing the graph in the…

Q: 1 1 11. Evaluate G-+y) dA, where R is the region bounded by the ellipse 4r²+ y² = 16. %3D R

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Q: Q4 Calculate the integral Se²y-2x (y + 2x)³ da Where R is the region formed by joining the vertices…

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Q: Consider the region bounded by the parabolas x = 8y^2 and x = 5 + 3y^2

A: Given parabolas equation-x=8y2  ....(1)x=5+3y2 ....(2)Solve equation (1) and (2) we get…

Q: 2- Find D xyz dV where D is the region with -1 ≤x≤1, x ≤ y ≤ 1, above z = x, and below z = y + 2.

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Q: Evaluate xydxdy over the region bounded by x axis, ordinate x = 2 and the curve y² = 4y %3D OA3 O B.…

A: To find: The value of ∫xydxdy over the region bounded by x- axis, ordinate x=2 and the curve x2=4y.…

Q: - The region bounded by 2y = x and (x − 2)² = −4y + 12 is revolved about the line y = 4. Determine…

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Q: 1. Evaluate I = D xy dA, where D is the triangular region with vertices (0,0), (0, 1), and (1,1).

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: 1. Find the centroid of each of the given plane region bounded by the following curves: y = 10x –…

A: We know that; The expression for the centroid is: x=1A∬xdydx &amp; y=1A∬ydydxWhere;Area=A=∬dydx…

Q: Calculate the Pntegrals over the defined region . y=-2x and y=1-2x on paralleberaM clased with Rhes.…

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Q: 2ху dx + (x + у) dy Jc C: boundary of the region lying between the graphs of y = 0 and y = 1 – x2

A: Given: ∫C2xy dx+(x+y)dy y=0 and y=1-x2

Q: 2. Evaluate [(3yz)dV where B is the region in the first octant lying below the plane x + 2y +2: = 4.

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Q: (c) Find II zdV where E is the region bounded by the cylinder y² + z² = 9 and the planes E x = 0, y…

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Q: SSR (r + y)2 dA, where R is the region bounded by the limaçon r = 2 + cos 0

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Q: -4 Evalate SS* dxdy, where D is the region bounded by the hyperbolas xy=2, xy=4 cMd the paraboles…

A: The given integral: Where D is the region bounded by the hyperbolas and parabolas We use change…

Q: 17. (2 +y +2) dx dy dz, W is the region bounded W by x+y+z= a (where a> 0), x = 0, y= 0, and z= 0.

A: We have to solve the integral and show the graph of question 17.

Q: x² and t %3D 2) = z where E is the region bounded by the parabolic cylinder y

A: We have to set up the integral according to the given information

Q: b.) xyz dv if S is the region bounded by the cylinders x² + y² = 25, x² + z² = 25 and the first…

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Q: (a) Calculate the centroid (7, y) of the region under the graph y = cos x for 0 < x <T/2.

A: Hi, since you have asked multiple questions, we will solve the first question for you. If want any…

Q: For numbers 8 - 15: Let M be the region bounded by the parabola y = x² and the line y = x +2. y = =…

A: The objective is to find the area of the shaded region.

Q: 1. Find So(r+2y)dA, where D is the region bounded by the parabolas y r, and y=1+

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Q: Let h(x, y) = 2x² – 2x²y + y². Find the absolute minimum and maximum values of the surface on the…

A: We use partial derivative to find critical points to check maximum and minimum value