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

Q: The area of the region bounded by y = v9 – x² , the x-axis and the line y=x in the first quadrant…

A: The area between the curves y=9-x2, y=x, x=0 :The area between curves is the area between a curve fx…

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

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Q: Find the volume of the solid generated by revolving about the line y=-1 the region bounded by the…

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Q: Find the area of the region bounded by the curve y = x2 + 3x + 2, x = 0, x = 2, and x axis

A: Solution

Q: Sketch the region of intearotion and evaluote. the integral. x2+y2e Vxz+ya dx dy 1n5 -n5)- y2

A: Consider the provided integral,

Q: FIND THE VOLUME OF THE SOLID GENERATED WHEN THE REGION BOUNDED BY THE CURVE (x-5)² = 4-Y AND THE…

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Q: Solve by integration: Find the centroid of the region bounded by y=x3+3 and the lines x=0 and y=0.…

A: given functions are                                              y=x3+3x=0y=0…

Q: Find the of the region bounded by the parabolas y – 6x = -x² and y + 2x = x² , area

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Q: Find the volume of the solid generated by revolving the region bounded by the |2x| about the x-axis.…

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Q: Find the volume of the solid generated by revolving the region bounded by the graphs 3) y = -x² +1…

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Q: Find the centroid of the region bounded by the graphs of y=x2 and x+y=6.

A: Given: The region is bounded by the graphs of y=x2 and x+y=6. We have to find the centroid of the…

Q: .Determine the distance from the y-axis of the centroid of the area bounded by the curve y = x³, the…

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Q: Find the volume of the solid generated when the region bounded by the curve (x - 5)² = 4 - y and the…

A: Given:-the region bounded byx-52=4-y  and the x-axisrevolving about the line x=2using cylindrical…

Q: Sketch the region of integration. (x, y) dx dy y y (0, 9) |(9,9) (0, 9) (9, 9) y=x y=x

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Q: Find the volume of the solid whose base is the region bounded between the curve y = x2 and the…

A: Given that the solid whose base is the region bounded between the curve y = x^2 and the x-axis from…

Q: Find the area of region that is bounded by the given curves. Integrate with respect to x and then…

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

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Q: Find the centroid of the region that is bounded by the line Y = 3X, the line X 2 and the X axis.

A: To find the centroid

Q: Find the exact coordinates of the centroid for the region bounded by the curves y = 4 – x² and y =…

A: The coordinates of the centroid of the area bounded under the curve of the function y=f(x) in the…

Q: Find the volume of the solid form by the region bounded by the lines y = 16 – x, y = 3x + 12, and x…

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Q: Find the exact coordinates of the centroid for the region bounded by the curves y=4−x^2 and y=0.

A: Given, y=4-x2, y=0 Here 4-x2=0⇒x2=4x=±2

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

A: The answer as follows:

Q: What is the volume of the solid generated when the region bounded by the graph of x = √y - 2 and the…

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Q: Find the volume of the solid in the first octant bounded by 2x + 3y + 4z = 12 and the coordinate…

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Q: Find the area of the region bounded by the curves x = y3 - y2 and the line x = 2y. %3D

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Q: find the volume of the solid generated when the region bounded by the curve (x-5)2=4-y and the…

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Q: sketch the described regions of integration. 0 ≤y ≤ 1, y ≤ x ≤ 2y

A: To sketch the regions of integration 0≤y≤1y≤x≤2y

Q: y= x°-2x² -3x +15 ,y=0,x=-1,x =3

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Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

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Q: Find the area of region enclosed by the curves. Hint: using integration y=lx²-4l and y=(x²/9)+4

A: The area under the curve: - Three easy procedures are often accustomed to figure the realm…

Q: Find the center of mass of a thin plate of constant density covering the given region. The region…

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Q: The line x=-3 of the region bounded by the 2x=4-y2 and 2x=y2-4 curves Calculate the volume of the…

A: We first sketch the region using a graphing calculator. 2x=4-y2 (red) 2x=y2-4 (blue) x=-3 (green)

Q: Find area of the region bounded by x² + y² = 5², 7y = -3x and 19y = 4x where y > 0. Leave your…

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Q: Determine the centroid of the area bounded by y^2=2x and the line x-y=0. pls show full solution…

A: to find the centroid of the area bounded by  y2=2x and x-y=0

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: 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: The area bounded by the line x=1 and the curve y^2-x=3 is revolved about the line y=4. Using Shell…

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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: Determine the area of the region bounded by y = xvx2 + 1, y = 1 e 2x, x = -3 and the y-axis.

A: First draw the region defined by these curves. If the region is bounded, then use the area under the…

Q: The region bounded by the curves y = x² – 2x and y = 4x is revolved about the line y = -1. Which…

A: The given curve is y=x2-2x and y=4x. Now, find the intersection point of these two curves.…

Q: Find area of the region bounded by x2 + y2 = 52, 3y = -2x and 20y = 8x where y 2 0. Leave your…

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Q: Sketch the region bounded by y =x² and x =y ( x 2 0) about the x-axis. %3D

A: Solve the following

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: Find the volume of the solid obtained when the region enclosed by the curve x=2-y² and find the x=y…

A: Draw the sketch of the given curve and lines.

Q: Find the centroid of the region bounded by the graphs of  y=4-x^2 and y=x+2

A: We use the Concept of Area bounded by region with the help of integration. And then find the…

Q: The volume of the solid obtained by revolving the region bounded by the curve y = x - x² and the…

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Q: The region is bounded by the curve y = 4x – x², y = 4 and the y-axis.

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Q: Find the area of the region enclosed by the curve y = 4x – x² and the line y = x using double…

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Q: Find the volume of the solid obtained by rotating the region bounded by y-2vx-1 and y=x-1 about the…

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