(b) Figure 1 shows the graph of y=x+ and y = x+1. The shaded region A, B and C 3 are the regions bounded by the graph. y 2 y? = x + 1 B C 1 y = Figure 1 Find the (i) total area of region A and C. (ii) volume of the solid generated by revolving region B about the x-axis. 1/3 寸--

Q: 8. Suppose you revolve the region completely about the of revolution. Describe the solid and find…

A: Introduction: A stable of revolution is a stable determine created via way of means of rotating a…

Q: 5. Find the volume of the solid obtained by rotating the region bounded by y =x² , x= 2, and y = 0…

A: In this question we have to find the volume of the region bounded by y=14x2, x=2 and y=0 about…

Q: Example 4: Find the volume of the solid generated by revolving the region bounded by y = x and y =…

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Q: 1. Find the area of the region bounded by the graphs of the equation y = x and y = x?. 2. Find the…

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Q: 4. Sketch the graphs of y = 4 + (x)½, x = 9 and y = 4. Shade the region bounded by the curves. Find…

A: To calculate the volume of the solid that is formed by revolving the below region about the x-axis…

Q: 7. Find the volume of the solid generated by revolving about the x-axis the region in the first…

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Q: 4. The region bounded by the curve y = x² + 1 and the line y = -x + 3 is revolved about the x-axis…

A: We have to find the volume of solid.

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

A: Given, y=ex, y=0,x=0 and x=2Around the line, y=-1 Recall the washer method to find the volume of the…

Q: 4. (a) Sketch the region bounded by the graphs of x = -2y, x = -1- y? and y = 0 (b) Set-up but do…

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Q: 1. Sketch the graphs of v = 2x - x2 and y = - x. Shade the region bounded by the curves, Find the…

A: Given, The sketch graph of; Y = 2x - x² Y = - x The volume of the solid that is formed by revolving…

Q: ermine the volume of the solid obtained by rotating the region bounded by y = √x and y = 3 and the…

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Q: 1. (a) Graph and shade the region enclosed by the curves y = x' - 1, y = 0 and x = 2. (b) Determine…

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Q: 1) The region bound by curves in the following: y=x, y=9x/1+x^3 Revolve the region about the line…

A: The two curves given in the problem are as follows: y=xy=9x1+x3 First, we will determine the…

Q: 1. find the volume of the solid resulting from revolving the region with the radius (2 – ½x)and -…

A: Please see the attachment

Q: a) Find the intersection point between curves 2=-2 and y=-/2x+2. Hence, find the area of the…

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Q: The region R bounded by the graph of y= 2sinx and the​ x-axis on (0.pi) is revolved about the line…

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Q: The diagram in Figure 3 shows the shaded region enclosed by the lines x = -1, x = 2 and the curves y…

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Q: 46. The region between the curve y = secx and the x-axis from *= 1 to x- 2 (shown here) is revolved…

A: Given the region between the curve y=sec−1x and the x axis from x=1 to x=2

Q: x=y2 x=2-y2 What is the volume of the shape formed by rotating the region bounded by its curves…

A: Integration of function expression with respect to variable x or y gives the area between function…

Q: a. Find the area bounded by the curves y=-x^2+4, and y = 0. b. Find the volume generated by…

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Q: EXAMPLE 2 Find the volume of the solid obtained by rotating about the x-axis the region under the…

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Q: Example 2 Determine the volume of the solid obtained by rotating the portion of the region bounded…

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Q: Consider the solid whose base is bounded by the x-axis and the curve y = f(x) = 9-x on the interval…

A: Here b=h

Q: 5. Find the volume of the solid obtained by rotating the region bounded by y = 2x – x² and y = 0…

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Q: 4. Figure 4 shows the region R in the first quadrant bounded by two curves y =(4 –x²) and y =(4- x²)…

A: The volume of solid formed by revolving the bounded area around y-axis is given by:…

Q: Consider the infinite region in the first quadrant bounded by the graphs of y = 1 /x2 , y = 0, and x…

A: Given : The infinite region in the first quadrant bounded by the graphs of y = 1/x2 , y = 0, and x =…

Q: Suppose that the region between the x-axis and the curve y = e-2x for x > 0 is revolved about the…

A: The region is between the x-axis and the curvey=e-2x for x≥0 is revolved about the x-axis.…

Q: 4. A solid is obtained by rotating about the x-axis. The curve is given to be as y = 3x2 – x³. Find…

A: Let's find.

Q: 1. y = 3x - x² and y = 3-x Find the volume of the solid generated by revolving about the line x = 4…

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Q: (b) The region bounded by the curve y = x² + 1 and the line y = 3 – r is revolved about the r-axis…

A: As per your query the solution of the problem (b) has been provided below.

Q: 2.1. Draw a triangle with vertices A(0, 1), B(2,0), C(3,4) and use integration to find its area.…

A: Given that, A triangle is drawn with vertices A(0,1), B(2,0), C(3,4)

Q: Consider the region R bounded by the curves y = ln(x)+1, y = –x+2, and the vertical line 5. (The…

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Q: 4. Find the volume of the solid generated by revolving about the line y=-3 the region bounded by the…

A: Using disc method, volume is evaluated.

Q: EXAMPLE 3 The region bounded by the curve y = Vx, the x-axis, and the line x = 4 is revolved about…

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Q: 9. Find the volume of the solid generated by revolving about the y-axis the region bounded by the…

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Q: 3. The line y = x + 2 and the parabola y = x contain a bounded region R between them. Find the…

A: Given, the line y=x+2 and y=x2

Q: x=y2 x=2-y2 What is the volume of the shape formed by rotating the region bounded by its curves…

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Q: A container is formed by revolving the region bounded by the graph of  y = x2 , and the x-axis, 0≤…

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Q: container is formed by revolving the region bounded by the graph of  y = x2 , and the x-axis, 0≤ x…

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Q: Determine that area. 4. A solid is obtained by rotating about the x-axis. The curve is given to be…

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Q: 4. The region bounded by the parabola y = x² and the line y = 2x in the first quadrant is revolved…

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Q: R is the region bounded above by the graph of f(x) = 6e-x² and below by the x-axis over the interval…

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Q: The region bounded on the left by the y-axis, on the right by the hyperbola x2 - y2 = 1, and above…

A: Given,The region bounded on the left by the y-axis, on the right by the hyperbola

Q: Q-1: Find the volume of the formed that generated by revolving the region bounded by the graphs y =…

A: given y=x-1y=x-12 graph of the region

Q: 46. The region between the curve y = sec ¹x and the x-axis from x = 1 to x = 2 (shown here) is…

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Q: 4. Consider the region bounded by the graphs of y = =x², y = 26, and x = 10 in the first quadrant.…

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Q: a) Find the points of intersection of the curves y = -3x? and y = 2x2 - 80. b) Find the Volume of…

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Q: b) […. obtained curve 1: Find the volume of the solid by rotating the region bounded by the y = -x²…

A: Given :y=-x2+9y=x2+1

Q: 4. Figure 4 shows the region R in the first quadrant bounded by two curves y =(4- x²) and y =(4- x²)…

A: