R is the region bounded by y = x², y = 4x - x² and the line x = and it is revolved about y = 0.

Q: Where is the centroid of the region bounded by y = 4-x2 and the x-axis?

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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: Let R be the region bounded by y = 5 sin(x , y = 5(x – 2)²,

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Q: Express the region as a union of Type I or Type II regions and evaluate the integral ffy dx dy. YA 1…

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Q: Calculate ff (2x + y) dydx, Where R is a region bounded x-y²-1 ,x=3,y=-1 and y=2 R

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Q: Calculate f 4y dydx, Where R is a region bounded by y=x* and y= - 3x2 - 2 R

A: Solution has been attached as an image

Q: Determine the area of the region bounded by 3x - 5y + 4 = 0 and y-axis from y = 2 to y = 5.

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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: The value of $ $(2xy - x²) dx + (x+y2) dy, where C is the enclosed curve of the region bounded by…

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

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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: The area of the region bounded by the z-axis and the curve = ²t - 1, y = 1-t² equals to: [2(1-1²)e²…

A: Solution

Q: Integrate f (x, y) = x over the region bounded by y = x, y = 4x − x^2, and y = 0 in two ways: as a…

A: First draw the graph of line y=x and parabola y=4x-x2. Then find the area of the intersection…

Q: rotate the region bounded by y=2x+1, x=4 and y=3 about the line x=-4

A: Solution:-

Q: 2. The area bounded by y = -(x – 1)² + 4 , and the lines x =1, y = 2, and y = 4 rotated about the…

A: Given: The area bounded by the curves which are: y=-12(x-1)2+4 and the lines x=1, y=2 and y=4 And…

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: The triangular region Ω has vertices (1, 1), (2, 0), and (2, 3).

A: My=∫12∫-x+22x-1kx2dydx

Q: consider the region in the xy plane bounded above by the curves y=x9/2 and y=x

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Q: The volume of the region bounded by x² + y² + z2 =1 is

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

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Q: 9. Consider the region bounded by the curves y = e", y = e¬¤ and y = 2. %3D

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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: Let S be the region bounded by the curves y = x and x = y²/2.

A: (a) Area of region bounded by given curves, S=∫02(2x-x)dx    (Area= ∫abf(x)-g(x)dx)

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

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Q: Calculate f 4y dydx, Where R is a region bounded by y=x* and y= - 3x2 - 2

A: Given integral is ∬R4ydydx, where R is a region bounded by the curve y=x2 and y=−3x2−2. We have to…

Q: Find the area of the region bounded by the graphs of the given equations. 1 y = 4x + y = 0, х %3D 1,…

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Q: integrate ƒ over the given region. ƒ(x, y) = x/y over the region in the first quadrant bounded by…

A: Given

Q: The region R is bounded by the curve with equation y = sin 2x, the x-axis and the lines TT x = 0 and…

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Q: The region is bounded by y = x³, y = 2x + 4 and y=-1. Then Arearegion= = ["f(x) dx + ["g(x) [*g(x)…

A: The region is bounded by y=x3, y=2x+4 and y=-1. Then Arearegion=∫abfx dx+∫bcgx, where a<b<c.To…

Q: Determine the absolute maximum and minimum values of f(x, y) = 2+4x–2x²+4y-y² on the region R…

A: The region bounded by the x-axis,y=3x and x=2 is:

Q: Find the centroid of the region bounded by the graphs of the inequalities

A: Given information: y≤14x2          ...(1)x-42+y2≤16              ...(2)y≥0                ...(3)

Q: Sketch the bounded region enclosed by 2y = 4/x, y = 3, and 2y + 3x = 7, then %3D find its area.

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Q: Find the area of the region cut from the plane x + 2y + 2z = 5 by the cylinder whose walls are x =…

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Q: Integrate f(x, y) = x over the region bounded by y = x 2 and y = X + 2.

A: This is the region. x2 = x + 2   x2 - x-2 = 0 x = 2 or x = -1 so , to integrating in the region.…

Q: Find a such that the line x = a divides the region bounded by the graphs of the equations into two…

A: Given, y2=4-xx=0

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

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Q: Find a such that the line x = a divides the region bounded by the graphs of the equations into two…

A: Given,    y = x,  y = 4  and  x = 0 So the region bounded by these curves is given by shaded region…

Q: 1- Integrate The furction F(X,y= over The region bounded byrj=X7y=2x9 x =1/X=?

A: According to our company guideline if multiple questions are posted we must do only first. You can…

Q: The region bounded by the curves y=1-x^3. ,y=e^x.  And the line y=3

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Q: R is the region bounded by y = -x² – 3x + 6 and x + y – 3 = 0 and it is revolved about x = -4.

A: Given that, R is the region bounded by y=-x2-3x+6 and x+y-3=0 and it is revolved about x=-4

Q: Define the region bounded by y = 0, y=4Vx , y = 24 - 2x and y = X -4 using vertical and horizontal…

A: The equations of the bounding sections are: y=0y=4xy=24-2xy=x-4 The equations are plotted on a…

Q: Q3. The region bounded by the curve y x² and the line y 3x, is revolved about the line x = -3. Find…

A: Here i use cylindrical shell method to find out volume of rotation

Q: Q3. The region bounded by the curve y = x² and the line y = 3x, is revolved about the line x = -3.…

A: We will find this using formula. As per our guidelines we are supposed to answer only one question.…

Q: Calculate S (2x + y) dxdy, Where R is a region bounded x=y"-1,x=3,y=-1 and y=2 R.

A: It is Given that, x varies from y2-1 to 3 and y varies from -1 to 3. To evaluate the integral,…

Q: The region is bounded by y = x³, y = 2x + 4 and y = -1. Then Arearegion = [*^f(x) dx + [²8(x) x +…

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