- Set up an integral that reprents the surface area of the figure generated by revolving the region trapped by y=3x x=-2, X=5, and 4=0 around the x axis. 5-4e2x+2 5eex,

Q: Q:- find the mass of the plate that bounded between the 2X 12 and the x-aris. if the plate densily…

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Q: 4) Set the integral that represents the volume of the tetrahedron bounded up by the planes 4r +y +3z…

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Q: - Consider the region R enclosed by the two curves: y = 2(x – 1)3 - I = (y/2)5 + 1 %3D (2, 2) R…

A: As per as our guidelines i am supposed to answer only three part of this question please re-post…

Q: Calculate the double integrals where L is the region in the first quadrant between the arcs of…

A: Use polar coordinate to solve it.

Q: Use an iterated integral to find the area of the region bounded by the graphs of y = 6x – x² and y =…

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Q: ey+eY 2

A: Please rate and feel free to ask any query about any part,

Q: 1) Write the integral to calculate the surface area of f (x, y) = 100 – x2 - y2 where z 2 19 Include…

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Q: Which of the following integrals represents the volume of the solid obtained by rotating the region…

A: We first sketch the region using a graphing calculator.

Q: Which of the following integrals represent the area of surface obtained by rotating the curve y= V1+…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Evaluate the given integral by making an appropriate change of variables, where R is the trapezoidal…

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Q: The area of the region outside the curve r=2+2cos0 and inside the curve r=3 is given by which…

A: Intersection points between two curves; r = 2 + 2 cos θ and r = 3 3 = 2 + 2 cos θ 1 = 2 cos θ cos θ…

Q: Sketch the region whose area is given by the definite integral. 50 40 30 20 10 6 6 50 40 30 y 20 10…

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Q: change the cartesian integral in an equvalant polor integral then evalute 2x-x² 1 the polor integral…

A: To change cartesian equation into polar, we use following substitutions x=r cosθy=r sinθdydx=r dr dθ

Q: (2, 4) y = 2x ng a vertical element of area, he area of the shased region is gven by the integral

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Q: Use an iterated integral to find the area of the region. 1 y = Vx - 7' 8 < x< 32 dy dx = y 2.0| 1.5…

A: Given, x is viaries as  8≤x≤32 And from the Graph y varies from 0 to y=1/√(x-7)

Q: Evaluate the integral by making an appropriate change of variables. 9 dA where R is the trapezoidal…

A: Consider the provided question,

Q: Evaluate the double integral I = SS dzdy over the region R = {(x,y)|3 <a < 5, 2 < y54} Enter the…

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Q: Set up an integral for the volume of the solid generated by revolving the region in the first…

A: We can see the region bound by the curves. Now we will set up the integral.

Q: Q5/ change the cartesian integral in an equvalant polor integral then evalute the polor integral…

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Q: Which integral below gives the volume of the solid of revolution obtained by rotating the bounded…

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Q: Q5/ change the cartesian integral in an equvalant polor integral then evalute the polor integral…

A: The given integral is ∫12∫02x-x21(x2+y2)2dydx. The objective is to change the cartesian integral to…

Q: xy Does there exist a positive number a such that the double integral over the rectangle defined by…

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Q: 16. Find the complete integrals of the foiowing equations: (i) z pq = p+4 che (i) p°q² +x?y? = x°q?…

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Q: Sketch the region of integration and change the order of integration for the integral .3 A f(z,1)…

A: Given problem:-

Q: Q3: Write triple integrals in the order (1) dzdxdy, (2) dxdydz, and (3) dydxdz to represent the…

A: Given The given curves are and .

Q: The area of the region {(x,y) ER² | -2≤x≤9, -3≤ y ≤ 4} is not equal to the double integral dxdy.…

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Q: Implement Green's Theorem for the curvilinear Integral of P xydx + (x2 + y7)dy in a square region…

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Q: Sketch the region whose area is given by the definite integral. xdx y 10 10 10 35 8 30 25 6 6 20 4…

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Q: Which of the following integrals represent the area of surface obtained by rotating the curve y= v1+…

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Q: Which of the following integrals represents the volume of the solid obtained by rotating the region…

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Q: 10. Use a triple integral to find the volume of the solid region in the first octant between: z = x?…

A: The given problem is to find the volume of the solid region in the first octant between the two…

Q: y. x= y? – 2 y = 1 x= e" y =-1

A: Given the graph of a region

Q: Q.5\(a)Use a double integral to determine the area of the region bounded by y = 1 - x2 and y = x? -…

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Q: Evaluate the integral by making an appropriate change of variables. dA where R is the trapezoidal…

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Q: Evaluate the integral by making an appropriate change of variables. 9 cos( 3 (Y-X)) dA where R is…

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Q: Which of the following integrals will give the volume of the the solid formed by revolving the…

A: Here we will find out the volume.

Q: Which of the following integrals represent the area of surface obtained by rotating the curve y= v1+…

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Q: a.) Find the area of the surface defined by 4x + 2y + z = 1, x² + y? < 1. b.) Evaluate the integral

A: Surface area

Q: -) Draw a diagram of the region of integration for the double integral: = ev/xdxdy Find the limits…

A: As per guidelines, we will solve only first question. Kindly repost other question separately.

Q: Set up the definite integral that gives the area of the region. Y1 = x2 – 5x Y2 = 0 dx 3 * 4 6 12,…

A: Area of the Region bounded by the curves :If f(x) and g(x) are two continuous function on a,b and…

Q: Which of the following integrals represent the area of surface obtained by rotating the curve y = v1…

A: Given : f(x) = √(1+4x) 1 ≤ x ≤ 5

Q: Set-up the double integral that will solve for the volume of the solid in the first octant bounded…

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Q: The region R is enclosed by the graph of y= 3x-x and the line y =x. If the region R is rotated about…

A: Curves are,  y = x   and    y = (3x - x2)   Hence,  x = 3x - x2  x2 = 2x  x = 0   or   x = 2…

Q: Evaluate the double integral a) dA, {R=(x,y) | 0 < y < 3 , 0 <x <y}

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Q: f. Set up (but do not evaluate) an integral with respect to x to represent the volume of the solid…

A: f) To setup an integral which represents the volume of revolution. x=(y-2)2⇒x=y-2⇒x+2=y⇒y=x+2

Q: Calculate a double integral of the figure, where R is the region bounded by y = x2 and y=2x. The…

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Q: SET-UP the double integral that solves for the volume of the solid z = 9 – x2 – y² on the first…

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Q: Sketch the region whose area is given by the definite integral. 9. 5 dx y3 1 3 4 3 35 35 30 30 25 25…

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Q: 1–q² (b) Interpret Vr2 + y? dydx as a volume and calculate the integral without integrating.

A: b)