1 The region bounded by y %3D %3D x*(x² + 2)2y = 0, x = 1, and x = 2 is revolved about the y-axis.

Q: 2. Find the area of the region bounded by the graphs of y = x2 – 6 and y-3 0.

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Q: What is the area (in square units) of the region bounded by the graphs of y=x2+2, and the x axis…

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Q: Find absolute extreme values of f(x,y) = 2xy² over the region R that is above the x-axis and bounded…

A: Given that f(x,y)=2xy2.

Q: 4. Find the area of the region bounded by the graphs of y = x3 + 6x, x = 0, x = 2, and the x-axis.

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Q: Determine the region bounded x=y2-6y+10 and x=2y+4

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Q: 16. Find the area of the region bounded by the graphs of the equations, y = -x² +x+ 6, y = 0

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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…

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Q: Find the area of the region bounded by the graphs of the equations. y = -x² + 6x, y = 0

A: Given equation y=-x2+6x,  y=0. The objective is to find the area of the region. "Since you have…

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: y = 4Vx +. 1 y = 0, x = 1, and x = 9

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Q: 29. Find the area of the region bounded by y =. = x2 + 3x + 1 and y = 6x - 1. [4.4]|

A: If two curves f(x) and g(x) defined over the interval [a,b], then the area bounded by the curves…

Q: 10. The region of integration D is bounded by y = 0 ,y = x² ,x = 1. Show that 1 - sin(1) xsin(y) dA…

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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: 1) Find the area of the region above the x axis and to the left of the line x = 1 bounded by the x…

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Q: Example 3 Find the centroid of the region bounded by y = x³, x = 2 and the x-axis.

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Q: 1: Find the area of the region bounded by the graphs of x = y², y = x + 3, y = -3 and y = 2.

A: The region is bounded by x=y2, y=x+3, y=-3 and y=2

Q: 2. The region bounded by x = 2 y, x = 0, y = 9 is rotated about the y - axis.

A: Given Data: The given curve is x=2y. Rotated about y axis. The limit for y axis is (0, 9).

Q: 3. Find the area of the region bounded by y=x²-2x +2 and y=6-x².

A: Use area under curve

Q: 3. Region bounded by Y = rotated about the x-axis ,x=0 and y=15,

A: By shell method

Q: 5. Approximate of region having given boundarics. Grea y=0 y= 3-In(1+x²)

A: Given query is to find the area bounded by the region.

Q: 9) Find the centroid of the region bounded by the graphs of y =-x“, y=0, and x=3.

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Q: Find the area of the region bounded by the graphs of the given equations. y =– x- 3' y = 0, x = 4, x…

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Q: Given y = 3x –- 2x +1, y =-x² + 2x +1 and a straight line y = 0.5x ; where x>0, 1. Sketch the curves…

A: Given y=3x3-2x2+1  , y=-x2+2x+1 and a straight line y=0.5x. We need to : 1) Sketch the curves and…

Q: Find the area of the given region y = tanh 2x

A: Given curve and figure: y = tanh 2x

Q: 4. Region bounded by y = x2, x=0 and y=15, rotated about the y-axis

A: Imagine the plot and rotate it about the axis specified and the resulting figure will lead to the…

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: 7 Find the area of the region bounded by the a graphs of f(x) = x+ 2x+1 and gix) = 3x+3. Write…

A: The given curves are: f(x)=x2+2x+1          and          g(x)=3x+3

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 X= (y-3)² and x= 16 about the x=-5

A: 1st we will find shaded region bounded by given curve and line

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: 1. Sketch a region bounded by the function ƒ (x)= x+1 the x axis and two vertical lines so that the…

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: 1. Find the area of the region bounded by the given curves. a) y = 2x° - x² - 5x + 4, y= - x² +3x…

A: We have to find the bounded area by curves

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: The region is bounded by the curve y = 6x – x² and y = x² – 2x –

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: x=y² – 4y (-3,3) wto rigin

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Q: 4. Region bounded by Y = x rotated about the y-axis ,x%30 and y=15,

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Q: 1-4 - Find the area of the shaded region. 1. yA y= 5x-x2 2. %3D (4,4) y= x

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: (4, 16) 10 Find the area of the region bounded by the graphs of y = 4x y = x2 and y = 4x. y = x2…

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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: Areas of regions Find the area of the following regions.

A: Given that, y=10x2-2x-24

Q: 1. Region bounded by y= x, x=0 and y=15, rotated about the x-axis

A: Volume of solid revolve around y axis

Q: Find the area of the region bounded by the graph of y = 2x2 − 3x + 2 the x-axis, and the vertical…

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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: 1. Find the area of the region bounded by the curve y = f (x) = |a² – 4| and the lines x = -3, and x…

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Q: 2) Find the absolute maximum and minimum for function F(x,y)= 4x³-2x²y+y² on the region R bounded by…

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Q: 8. Consider the region bounded by y =- * , y = Vx, x=1. х

A: Let us consider the curve y=f(x) and y=g(x) The area under the curve y=f(x) and y=g(x) in the…

Q: 1. Determine the area of the region under the curve y=x√(x² - 1) 2. Determine the area of the region…

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