4. A solid has a base that's bounded by y = Vsin(x) and the x- axis from x = 0 to n. The cross-sectional areas perpendicular to the x-axis are half-circles as shown. Set up the integral and solved for the volume based on the Cavalieri-principle %3D co-antians : lalf circles.

Q: 2. Find the volume generated by revolving about the y-axis, the area bounded by x² + y² = a² and x+y…

A: The bounded region: Green colored    To find: The volume of revolution around y-axis of the bounded…

Q: Suppose the following region is rotated around the y-axis to create a three dimensional solid. 4- 3-…

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Q: Let A1 be the region bounded by y = 5x (1−x) 2 and the x-axis between x= 0 and x= 1. Find the…

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Q: 7. Find the volume of the solid obtained by rotating the region under the graph of f (x) = 9 – x2…

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Q: 1) Find the volume of the solid cut from the first octant by the surface z=4-x2-y.

A: As per our guidelines we are supposed to answer only first question. Kindly repost other question as…

Q: 2. Solve for the volume of solid of revolution formed by rotating the area bounded by y = x² + 2, x…

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Q: 2. Find the volume of the solid generated when the region bounded by y = x2 - x and y = x- x2 is…

A: First of all for calculating the volume of the solid revolving around any particular axis, graph…

Q: 27. Find the volume generated by rotating the area bounded by y = x² + x, x = 1, x = 4, and the…

A: Given that: y=x2+x,   x=1,  x=4   and   the   x-axis To sketch the graph,

Q: The region enclosed between the curve y²= kx and the line x = ¼k is revolved about the line x = ½k.…

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Q: In the given question as follows, find the volume of the solid generated by revolving the region…

A: Definition used -                     Washer method -                     v=π∫ab(f2(x)-g2(x))dx…

Q: 5. Find the volume of the solid in the first octant bounded by the two cylinders x²+y²=4 and…

A: I am attaching image so that you understand each and every step.

Q: The area bounded by y = x² and y = 2 – x² is revolved about the x-axis. Find the volume of the solid…

A: We have to find volume of solid revolution.

Q: The volume of the solid obtained by rotating the region enclosed by 5x y = e° + 5, y = 0, x = 0, x =…

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Q: 4. Find the volume of the solid obtained by rotating about the y-axis the region bounded by y = 2x2…

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Q: 16. Find the volume of the solid generated by revolving the region enclosed by y = 3sinx and y = 0…

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Q: 2. Find the volume of he solied nohose base is Ine region bounded by y-x And y=1-x2, and whose are…

A: The points common to y=x2 and y=1-x2 can be calculated as: x2=1-x22x2=1x2=12x=±12 So the integral is…

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: The volume of the solid obtained by rotating the region bounded by y=4-x, y=0, X=-2, x-2 about the…

A: Determine for true or false

Q: 7) Suppose that y, =sinx and y, = cos x on [0,4] %3D Find the volume if the region between y, and y,…

A: First we sketch the region using a graphing calculator The shaded region is rotating about the x…

Q: Consider the region bounded by the graph of y2 = (6 – x)2 (1 + x)2 on the interval [o, 1]. Find the…

A: Given: y2=6-x21+x2 To Find: The volume of the solid generated by revolving the region about the…

Q: The volume of a solid is described by the double integral L 3 x’y dydx If the order of the integral…

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Q: What is the exact volume of a solid that is formed with a square base, aligned with the center of…

A: Now we will find the volume using the integration

Q: 4. Use the washer method to determine the volume of the solid obtained by the revolving the region…

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Q: Only one of these calculations is correct to evaluate the volume of the solid generated by revolving…

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Q: 9. Find the volume of the solid obtained by rotating the region bounded by y = Vx. x 0, and x = 4…

A: To find: The volume of the solid obtain by rotating the region bounded by y=x, x=0 and x=4 about the…

Q: 6) consider the area between the X-axis and the curve y= Sin2x for O< Xs#/2. when this area is…

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Q: 3. Find the volume of the solid formed by y = √√4sin(x) bounded by x = 0 revolved about the x axis…

A: According to the question we need to find out the volume of revolution of the curve.

Q: 4. Set up a (sum of) definite integral(s) that is equal to the volume of the solid whose base is R…

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Q: 2) ( ) Sketch and find the exact volume of the solid obtained by rotating the region B bounded by…

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Q: 1. Find the area bounded by y= (11 - x)1/2, the lines 3x = 2 and x = 10, and the X-axis. 2. Find…

A: The given problem is to find the area between given curves and also find the volume of solid…

Q: find the volume (in units 3) generated when the region between the curves is rotated around the…

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Q: 4) Find the volume of a solid generated by revolving about the x- axis the region bounded by y = x2…

A: We find the volume of a solid generated by revolving about the x- axis the region bounded by y = x2…

Q: Find the volume generated by rotating the region between the graphs of y = 2 - x, x = 0, and the…

A: Consider the provided region, y=2-x,x=0 Find the volume generated by rotating the region between the…

Q: 1 3) Consider the region bounded by the graphs of y =-x, y= V4-x , and y=0. 3 c) If this region is…

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Q: The area bounded by y = x3 + 2x + 1, x = 1 and x = 3 is to be revolved about the x-axis. Find the…

A: Given problem:- The area bounded by y = x3 + 2x + 1, x = 1 and x = 3 is to be revolved about the…

Q: 1. Use your preferred method to calculate the volume of the solid obtained by revolving the region…

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Q: 2. Set up the integral(s) for finding the volume of the solid of revolution obtained by rotating…

A: We will find out the required volume of solid of revolution.

Q: Find the volume of solid generated if the area bounded by each of the following curves is revolved…

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Q: Find the volume of the solid of revolution generated by revolving about the x-axis the region under…

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Q: If the area bounded by the parabola y = x² and the line y = x is revolved about the x – axis, the…

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Q: The volume V of the solid formed by revolving the region bounded by the graphs of y=VE-2, y-0and…

A: Let us first find the volume V of the solid formed by revolving the  region bounded by the graphs of…

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: What is the exact volume of a solid that is formed by rotating the region, enclosed by the functions…

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Q: Calculate the volume of the infinite solid obtained by rotating the region under y = (x2 + 1) −2 for…

A: Use shell method and find the volume.

Q: 18. Find the volume of the solid obtained by revolving the region under the graph of y = 5- on [1,…

A: To find the volume of the solid obtained by revolving the region under the below graph on [1, ∞)…

Q: 2. Find the volume for the solid generated by taking the area enclosed by f(x)=cos(x), x=0, x = and…

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Q: 5. Find the volume generated by the areas bounded by the straight line y = x, between y = 0 and x =…

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Q: Only one of these calculations is correct to evaluate the volume of the solid generated by revolving…

A: Here we have to set up the required integral.

Q: 1. Sketch the region enclosed by the curves of y = x² – 2x. y=x+4, x =-2, x = 5 and find the area of…

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Q: 6) Use the washer method to find the volume of the solid generated by revolving the region y = x² +1…

A: We first sketch the region using a graphing calculator. From the graph, we see that x is from 0 to…