R is the region bounded by y = 4 – x² and the x-axis and it is revolved about y = 4.

Q: Find the area of the region bounded above by y AY -x² + 8 and below by y = x². ==

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Q: find the region bounded by x= Y-y3 ,X=1 = 1 Y=L, revolved about o X- axis

A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Evaluate y'dx+ xydy where C is the boundary of the region bounded by y = Vx.y 0, and x 9.

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Q: 4. Find the area of the shaded region by integrating with respect to 'y', y-2x-4 1.-2)

A: The area between two curves f1 and f2 between the points y=a to y =b is given by; A=∫ab(f2-f1)dy

Q: Evaluate (2r+y) dV _ where V is closed region bounded by the z= 4>x and the planes x = 0, y = 0 and…

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Q: Evaluate Slo I –dA, y3(x3+1) where D is the region bounded by x = -y³, х%3D 3 аnd the x — аxis. |

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Q: Evaluate the moment M, and M, of the region bounded by y = 2x + 1, x + y = 7 and x = 8.

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Q: Rotate the region bounded by y = 6e 2" and y = 6+ 4x - 2x between a = 0 and a = 1 about the line y =…

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Q: Evaluate || 5x cos y'dxdy where S is the region bounded by y = 2 and 1 x and the y-axis. 4 y =

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Q: Evaluate the moment M, and M,y of the region bounded by y = 2x+ 1, x + y = 7 and x = 8.

A: fx = y = 2x+1gx= y = 7-x      Mx=12∫LLULfx2-gx2dx               Moment about x-axisMy=∫LLULxfx-gxdx…

Q: Evaluate xydxdy over the region bounded by x axis, ordinate x = 2 and the curvex² = 4y %3D OA 3 О В.…

A: The shaded region shown in the figure is the area of integration

Q: Sketch the region enclosed by the given curves. x = 7y2, x = 4 + 6y2

A: Here, We will use the concept of tracing the simple curve, and method of double integral to find the…

Q: R is the region bounded by y = 4 – x2 and the x-axis and it is revolved about y = 4.

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Q: The region between the graphs of y = x² and y = 3x is rotated around the line x = 3.

A: Given data:   The expression first curve is: y=x2. The expression for the second curve is: y=3x. The…

Q: Sketch the region D = {(x, y, z): x2 + y2 ≤ 4, 0 ≤ z ≤ 4}.

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Q: Determine the area of the region bounded by x = y² – y – 6 and a 2y + 4.

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Q: Find the area of the region bounded by the curves y = x² and y = - x² + 4x. 9/4 11/3 12/15 8/3 none…

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Q: The region R is bounded by y 4 %3D and y = x +3. -

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Q: The area bounded by the curve z = y.y-axis and the lines Y3D0. y32 is s

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Q: (b) |(x+y)dA} where R is the region bounded by y=Jx and y = x² .

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Q: The area of the region bounded by the curves y = 3x – x² and y = 2x is 5 а. 3 O b. 32 3 С. d. 1 6.…

A: We need to find the area of region bounded by the given curves. For that, we need to find their…

Q: The area of the region bounded by y=x2+2, y=−x, x=0 and x=1 is

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Q: 3. Find f 6y(x + 6) dà where D is the region bounded by x = - -y? and x = y - 6.

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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: he region bounded by x2 + y2 = 4?, 4y = -5x and 13y = 6x where y 2 0. Leave your answer correct…

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Q: y = x³ + 2x? – 8x, y = x³ + 5x? -

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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: Find the area of the region bounded by the curve y2=4x and the lines x = 1 and x = 4.

A: The given curve is y2=4x and lines x=2 and x=4. From the given information,

Q: Consider the region bounded by the Xxy curves J 3-2x, and y=3, %3D

A: Calculating the area of the region bounded by the curves

Q: Rotate the region bounded by y= x- 2x + 4 and y X+14 about the X- axis

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Q: Determine the area of the region bounded by x = y² – y – 6 and 2y + 4.

A: According to the fundamental theorem of calculus ∫abf(y)dy=F(b)-F(a), where dFdx=f(x). The equation…

Q: and the y-axis. 2. Evaluate , 5x³ cos(y³) dA, where D is the region bounded by y = 2, y =:

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Evaluate the moment M, and M, of the region bounded by x = 2y - y2 and the y=axis.

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Q: Evaluate the moment M, and My of the region bounded by x- 2y - y? and the y-axis.

A: Given area is bounded by x=2y-y2 and y-axis.  On the y-axis, x=0. We try to find the point of…

Q: Sketch the region bounded by the graphs of y%3= 1 and y=D4-3x, then find its area.

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Q: Find the area of the region bounded by = y ; x=2y²_4

A: The given functions are x=y2 and x=2y2-4 To find the area enclosed between the curves.

Q: Q/ Evaluate (1Ox²y³-6 dA of D where D is the region bounded by : x = -2y? and x = y3.

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Q: The region D bounded by y = 0 and y = -1+a² is shown in the following figure. Is this region of Type…

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Q: Find the area of the region bounded by y = Vx- 5 and x – 3y = 3. O 1 9. O 1

A: We have to find solution

Q: Find the area of the region bounded by the graphs of y = x2, y= x² – 2r +3 and y= 2x- 1.

A: Given curve is y=x2, y=x2−2x+3 and y=2x-1 we have to find the area of the region bounded by the…

Q: Evaluate where D is the region bounded by the semicircle x = /4– y² and the y-axis.

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Q: The numerical value of л за 3dA (where D is the region bounded by lines y=0 and x = 1, D and the…

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Q: 2. Evaluate Vye"V dA where D is the region bounded by y = x² and y = 4.

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Q: Find the value of k between –1 and 2 such that the area of the region bounded by the lines y = -x, y…

A: we know that the area of a triangle with vertices A(x1, y1), B(x2, y2) and C(x3, y3) is given by…

Q: O R is the region bounded by x² + y – 4 = 0 and x – y +2 = 0 an is revolved about y = 0.

A: We use washers method to find the integral of that evaluate the volume of the solid of revolution.

Q: Find the area of the region bounded by one loop of the curve x2 y*(1 – y²)

A: Given:          x2=y41-y2         x=±y41-y2         x=y21-y2 The graph is symmetric about the…

Q: What is the area of the region between  y=x^2 -2x-3 and the x-axis from x=0 to 6?

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Q: Determine the area of the region bounded æ = y2 – y – 6 and a = 2y + 4.

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Q: Find the area of the given region y = sech (x/2)

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