Find the absolute maximum and minimum values of f(x, y) = 4 + 2x2+y2on the region R={(x, y)|−1≤x≤1,−1≤y≤1}.

Q: sketch the described regions of integration. 0≤y ≤ 8, 1/4 y≤ x ≤ y1/3

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Q: The region is bounded by y = x³, y = 2x + 4 and y = -1. Then Arearegion = [₁ f(x) dx + ["40 + [~…

A: Here in this question, three curves are given and we need to find out the limits of integration, and…

Q: Sketch and shade the region y = x² – 1, hence find the total area between the given curve and the…

A: The standard form of a parabolic function is where (h, k) is the vertex. This standard form is also…

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: The region between y=x+3 line and yax+l curu a) x -axis 6) y=1 line cX=-1 line

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Q: Sketch the region R of integration and switch the order of integration. 8. f(x, y) dx dy 8. 8. 2- 6.…

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Q: The region between the graphs of y=x^2  and  y=3x is rotated around the line x=3 The volume of the…

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Q: Sketch the region R of integration and switch the order of integration. 49 f(x, y) dy dx 50 3 40-…

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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 bounded by y = 3x – x² and y = -x %3D

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

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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: Sketch the region of integration. [ [² x√ 1 + y³ dy dx

A: The answer as follows:

Q: 3. The region bounded by y = x³, y = x, x > 0 is rotated about the x – - axis.

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

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Q: y =-z +4x, y= 0

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Q: The area D is the area in the XY-plane bounded by the X-axis, Y-axis, and the 4x + line 5y = 0.…

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Q: Find the area of the region bounded by the graphs. 1. y=x',y=Vx 2. y+x = 6, y+2x-3 = 0 3. 2y = x+…

A: Area enclosed by bounded region  y=x^2 , y=√x A=1/3 sq units

Q: The extreme values of Ax, y) = 4x + 2y? on the region x +y <4 are %3D O A. Maximum = 24, Minimum = 0…

A: Consider the given function whose extreme values is to calculate.

Q: Find the area of the unbounded shaded region. 3 y = V2 - x y 3.0 2.5 2.0 1.5 1.0 0.5 -5 -4 -3 -2 -1

A: In this question we have to find the saded area in the figure with the help of integration.

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: find the absolute maximum and minimum values of ƒ on the region R. ƒ(x, y) = x2 - y2 - 2x + 4y R:…

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Q: The region is bounded by y = x³, y = 2x + 4 and y = −1. Then Area region = [ f(x) dx + √ f(x) dx +…

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Q: ( ) The region between the graphs of y = x2 and y = 2x is rotated around the line x = = 2. The…

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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&lt;b&lt;c.To…

Q: Find area of the region bounded by x2 + y2 = 32, 6y = -6x and 20y = 6x where y 2 0. Leave your…

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Q: integrate ƒ over the given region. ƒ(x, y) = 1/(xy) over the square 1&lt;=x&lt;= 2, 1 &lt;=y&lt;=2.

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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 area of the region bounded by y = 5-x2, y 2x + 2, y=-x-1, a. in terms of x b. in terms of y…

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Q: Use the method of partial fractions to find the area bounded by the curve y

A: The given function y -y = 2x-8x2-5x+6y = 2x-8x2-2x-3x+6y = 2x-8x(x-2)-3(x-2)y = 2x-8x-2x-3Using…

Q: Sketch the region R of integration and switch the order of integration. V 36 - x2 f(x, y) dy dx 4. 4…

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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, y2=4-xx=0

Q: While evaluating the area of the region bounded by two curves y√=xy=x and y−15x+54=0y−15x+54=0, the…

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

A: Given regions are, y=x2y=4x-x2y=0 Now, using Washer method by the formula, V=π∫abR2-r2dx

Q: Find the area of the region bounded by the graphs of the equations. y = Vx(4 - x), y = 0

A: Sketch the area of the region bounded by the graphs of the equations y=x4-x and  y=0 as shown below.…

Q: 7. Find the centroid of the region bounded by the graphs of Vx + Vy = va; x = 0; y = 0

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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: Find the maximum and minimum of f(x, y) = xy-x+y-1 on the region: x^2+y^2 &lt;= 4.

A: A scalar function f(x,y) is a rule that is used to associate a number, or quantity with a particular…

Q: 3. Find the area of the region bounded by the curve y = Vx – 1, the y - axis and the lines y=1 and…

A: Simplify the equation y=x-1 to obtain the expression of x. y=x-1y2=x-1x=y2+1 Draw the graphs…

Q: find the absolute maximum and minimum valuesof ƒ on the region R. ƒ(x, y) = x2 + xy + y2 - 3x + 3y…

A: Let us consider the given function, f(x, y)=x2+xy+y2-3x+3y .....(1)  The triangular region cut from…

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 = [₁ f(x) dx + f[ g(x) dx,…

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

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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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Q: While evaluating the area of the region bounded by two curves V/y = x and y – 10x + 21 = 0, the -…

A: We will find interesting points.

Q: Region bounded by y=Vx, x=0, and y=2

A: We have to find out the volume of the given solids.