8. Using the cylindrical shell method, find the volume generated by revolving about the x-axis the area bounded by the curves y = -x and y = 3. Include x=0 or y-axis as part of the boundary of the area being considered

Q: 3. Find the volume generated by revolving about the y - axis the area bounded by the curve y = sin x…

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Q: 18. Use Cylindrical shells method to find the volume of the solid that results when the area of the…

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Q: 2. (a) Based on the diagram 1, find the intersection points between curves y=r' and Hence, find the…

A: The point of intersection of two curves is the place where the two curves meet.y=f(x) To find the…

Q: 8 Consider the region bounded by y = , y = Vx, x=1. Make sure to draw the appropriate sketch of the…

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Q: 8. Using the cylindrical shell method, find the volume generated by revolving about the x-axis the…

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Q: 5.) Find the volume generated by revolving the area bounded by the curve y2=4x, x = 0 about the line…

A: Given area is bounded by: y2=4x and x=0. The area is revolving around the line y=4. From y2=4x we…

Q: 5. Evaluate using the circular disk method. Find the volume of the solid formed by revolving the…

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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 curve represented by y = x? from (0, 0) to (1, 1) is rotated about the x-axis, what is the…

A: Let us consider the 5th question 5.

Q: b) Find the volume (using cylindrical shell) generated by revolving the region x y3 and y=x-2 about…

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Q: 7. Using the circular disk method, find the volume generated by revolving about the x-axis the area…

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Q: 1. Find the volume of the solid generated by revolving about the indicated axis the area bounded by…

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Q: 5. Find the volume of the solid generated by revolving the region bounded by y = e-x², the x-axis,…

A: The given equation is y=e-x2. Find the volume of the solid rotated about the y-axis.

Q: 1. Find the volume generated by revolving the area bounded by the curve y = (1 – x²)² and the x–…

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Q: Use the method of cylindrical shells to find the volume V generated by rotating the region bounded…

A: Explained below

Q: 4) Using the appropriate method, find the volume generated by revolving the plane bounded by y - 3 =…

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Q: 5) Using the appropriate method, find the volume generated by revolving the plane bounded by the…

A: Image is attached with detailed solution.

Q: 5. Find the volume of the solid generated by revolving about y axis, the area bounded the y=(x²-4)²…

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Q: Determine the surface area formed by revolving the shaded area 360∘ about the z axis.

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Q: Find the volume formed by revolving about the line x = 1 the area bounded by the curve y = (x2– 1)2…

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Q: 1. Find the volume generated by revolving about the x-axis the area bounded by the lines y 2x + 1, y…

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

A: Given curve is x=5y+1,x=0, y=0, y=3 We have to find the volume of the solid generated by revolving…

Q: 1. Use Cylindrical Shell Method to find the volume of the solid generated by revolving the region…

A:

Q: The area bounded by the parabola ay = x2 and the line y = b is revolving around the x-axis. Find the…

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Q: 3. Use the method of cylindrical shells to find the volume generated by rotating the region bounded…

A: Given : The curves are : y=-x2+2x+3, x+y=3 We have to find the volume generated by the given curves…

Q: Find the volume of the solid generated when the region ? bounded by the given curves is revolved…

A: Find the volume of the solid generated when the region ? bounded by the given curves is revolved…

Q: 7. Using the circular disk method, find the volume generated by revolving about the x-axis the area…

A: Explained below

Q: 3. Compute the volume of the solid obtained by revolving the area between the graphs of y = x² and y…

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Q: 4) Using the appropriate method, find the volume generated by revolving the plane bounded by y - 3 =…

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Q: 5) Using the appropriate method, find the volume generated by revolving the plane bounded by the…

A: To find the volume of the solid generated by revolving the region bounded by the below curves about…

Q: 2) The region bounded by the curve y = , the r axis and the line r = 1 is revolved about a- axis to…

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Q: 2- Find the volumes of the solids generated by revolving the region bounded by The curve x = y - y3…

A: We will find region bounded and the solid of revolution . To find volume we will use cylindrical…

Q: The curve y = Vx, the line x=2, and the x-axis form the sides of a bounded region R. Find the volume…

A: Drow the given curves on coordinate plane and imagine the solid after rotation about x-axis and form…

Q: 4. Find the volume generated by revolving about the y - axis the area bounded by the curve y = sin x…

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Q: 24. Find the volume formed by rotating about the y -axis the region enclosed by: x = 9y and y3 = x…

A: Here, the curves are x=y3 & x=9y. Now, the points of intersections are at: y3=9y⇒y=0,3   because…

Q: 1. Find the area bounded by the curve y = x^2  and the x-axis and the ordinates x = 0 and x = 2 2.…

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Q: 5. Use cylindrical shells to find the volume of the solid generated when the region enclos between x…

A: The formula for the volume of the solid generated by a curve using the shell method is given by…

Q: 5) Using the appropriate method, find the volume generated by revolving the plane bounded by the…

A:

Q: 6. Use cylindrical shells to find the volume of the solid generated when the shaded region is…

A: Here is the solution of the given problem. Cylindrical Shell Method to find out the volume of a…

Q: 5) Using the appropriate method, find the volume generated by revolving the plane bounded by the…

A:

Q: Find the Volume generated by revolving the area bounded by the given curves and lines revolved about…

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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: 1. Use Cylindrical Shell Method to find the volume of the solid generated by revolving the region…

A: According to our guideline we can answer only first question and rest can be repost.

Q: 5. Find the volume of the solids generated by revolving the regions bounded by the curve y = sec y =…

A: Here, the region bounded by the curve y=sec x, y=0  from x=-π4 to x=π4 about x-axis is:

Q: Y = x- 5x + 6 y=0 revolved about the y-axis

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Q: 5. Find the volume of the solid generated by revolving about the x-axis the region bounded by the…

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

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Q: 6. Find the volume of the solid generated when the area of the region between the curves y = Vsinx,…

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Q: 5/ Find the volume of the solid generated by revolving the area enclosed by y= x², y-0, x-1 about 1)…

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Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.