2.1. Draw a triangle with vertices A(0, 1), B(2,0), C(3,4) and use integration to find its area. 2.2. Sketch the region enclosed by y= vVI-1, 1-y 1 and calculate its area. 2.3. Find the volume of the solid generated by revolving the region in 2.1 above about the y-axis.

Q: 3. Find the exact value of surface area of the solid that is described by the intersection of the…

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Q: 4. A semi-circular disc is situated in region r2+y² < 25 and x<0 of the ry-plane. If the mass…

A: Consider the region as drawn in the figure below: The shaded region in polar coordinates is given…

Q: b) 1: Find the volume of the solid obtained by rotating the region bounded by the curve about the…

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Q: 2. Find the volume of the solid lying under the elliptic x2 paraboloid + 4 y2 +z = 1 and above the…

A: The elliptic paraboloid can be expressed as z=f(x,y) where fx,y=1-x24-y29. We have to notice that…

Q: d the volume V of the solid obtained by rotating the region bounded by the ren curves about the…

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Q: b) y = 1<x< 4 about the y-axis

A: To find the volume of the solid obtained by rotating the given region about the specified line y=1x…

Q: 4. Find the volume of the solid generated by revolving the first quadrant area of the curves xy=2,…

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Q: THE REGION BOUNDED BY 2y = x AND (x-2)² = − 4y + 12 15 REVOLVED ABOUT THE LINE Y = 4. DETERMINE THE…

A: Introduction: The washer method refers to this application of the slicing method. Because the slice…

Q: 1. Find the area bounded by the curves y = x², y=A and x=B. 2. Find the volume of the solid…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: For the region bounded by the curves y = 2v/x, and y = 2 x2, find the following: 1. The area of the…

A: Area and volume

Q: 1. Use the shell method to find the volume of the solid of revolution generated by revolving the…

A: Given: y=3x, x axis, x=1 , x=5  To find: volume using shell method about y axis

Q: (3+ In x)² Find the volume of the solid when the curve y=- is rotated 360° about the x-axis between…

A: Here, the function is y=f(x)=(3+ln x)32x12. The volume obtained by rotation is given by…

Q: Example 1: The region between the curve y= /x, 0<x< 4, and the x-axis is revolved about the x-axis…

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Q: D. 48. Find the volume of the solid obtained by rotating the region bounded by y = 3Vx and x = 4…

A: First, we sketch the region using a graphing calculator. The shaded region will rotate about the…

Q: 4. Find the volume of the solid obtained by rotating about y ax[is the re[gion between y=x^2 and…

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Q: 5- Find the volume of the solid generated when the region bounded by the curve x cos y and the lines…

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Q: 20 4 18 16- 14 12- 10- Y = (x- 2)4 6 - 21 2. 3, 00 4.

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Q: Consider the region on the 1st quadrant bounded by y = √4x²,x and y- axes. If the region is revolved…

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Q: If the region under the graph of y = 3x +4 from a axis, then the volume of the resulting solid is 2…

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Q: 1. Sketch the region enclosed by y = y = 0,x = 1,x = 5. Find the volume of the solid x2 obtained by…

A: Sketch the region enclosed by the given curves:

Q: 5.5 Find the volume of the solid bounded above by the graph of f(x, y) = xy sin(x²y) and below by…

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Q: 24 22. Find the volume generated by revolving about Ox the area bounded by the Ans. ra³. hyperbola…

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

Q: 1. Find the area bounded by the curves y = x², y=A and x=B. 2. Find the volume of the solid…

A: Firstly, find the area bounded by the curve y=x2, y=16 and x=5. That is the area between the upward…

Q: 5) Find the volume of the solid obtained by rotating about the X axis the region described in…

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Q: 7.3 5. Use the shell method to set up and evaluate the integral that gives the volume of the solid…

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Q: 13. The region bounded by y = x°, y = 0, and x = 2 is revolved about the line x= 2. Find the volume…

A: Formula: The volume of the solid revolution generated by using disk method is given by,…

Q: :- Find the volume of the solid between y = x+1 which obtained the curves y = (x-1)² and by rotation…

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Q: 1 Find the volume generated when the area bounded by y=√√x and y=-x is rotated around the x-axis 2…

A: The region bounded by y=x and y=12x is rotated about the x-axis.

Q: = 1 + 16 9. revolving (#1) Find the volume of the solid bounded by about the x-axis:

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Q: 1. Find the volume of the solid obtained by rotating the given region about the specified line.…

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Q: 1. Find the area of the region bounded by the parabola x = 3+ 2y - y? and the line 2x + 3y = 6. Find…

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Q: - The region bounded by 2y = x and (x − 2)² = −4y + 12 is revolved about the line y = 4. Determine…

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Q: (b) (2 pts. each) Set-up only the integral that will give the volume of the solid generated when the…

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Q: 3. Find the volume of the resulting solid of revolution located in the first quadrant bounded by the…

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Q: 1 Find the volume generated when the area bounded by y=√√x and y=-x is rotated around the x-axis 2 A…

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Q: 5. Find the volume of the solid formed by revolving the region bounded by the graphs of y = 3 – x²…

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Q: 8. (a) Find the area enclosed by the curves y = x2 – 4 and y (b) Find the volume of the solid that…

A: (a).  The area between the given curves is: Area=∫-172 5x2-12-x2+4 dx

Q: 16 12 8 0 2

A: Given problem :- Consider the solid of revolution obtained by revolving about the x-axis the region…

Q: Find the volume of the solid generated by revolving the region bounded by the given lines and curves…

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Q: 1. Find the volume under the parabolic f(x,y) = x²+ 4y² and above the rectangle R :0 < x < 1,1 < y <…

A: Given  fx,y=x2+4y2

Q: 1.Use cylindrical shells to find the volume of the solid generated when the region enclosed by the…

A: In the question it is asked to calculate the volume of solid generated using cylindrical shells.

Q: 1. Consider the region bounded by y = x and y = Vx, shown below. Find the volume of the solid…

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Q: could i please get help with 9c?

A: Graph the given functions using graphing calculator. Shade the bounded region. It will rotate about…

Q: 14. Find the volume of the solid created by revolving the shaded region given below about the x axis…

A: Here given a straight line x+2y=2 and it is revolved around x axis. We need to compute its volume.If…

Q: Consider the reg. A enclosed by the curves y = x2 +1 and y = 2x + 1: 2 The volume of the solid…

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Q: 3) Find the volume of the given solid: Under the surface z = 8ry and above the region enclosed by…

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Q: 1. Find the volume of the solid in the first octant bounded by the coordinate planes, the plane x =…

A: Note: Hi! Thank you for the question As per the honour code, We’ll answer the first question since…

Q: . a) Find the volume of the solid enclosed between the paraboloids z = 5x^2 + 5y^2 and z = 6 − 7x^2…

A: Given:   the paraboloids z = 5x^2 + 5y^2 and z = 6 - 7x^2 - y^2

Q: Find the exact volume V of the solid obtained by rotating the region enclosed by the graphs of y = e…

A: The given region enclosed by the graphs: y=e-x, y=1-e-x The graph of the above region:           To…

Q: 12. Find the volume of the solid generated by revolving the region bounded by the curve y = sin x…

A: F(x) = sinx-2