48. Find the volume of the region bounded by y = 1 – x², z = 1, y = 0, and z + y = 2.

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: Find the volume of the region bounded by z = 40 − 10y, z = 0,y = 0, and y = 4 − x 2.

A: z = 40 − 10y, z = 0,y=0 and y=4-x2The region is plane z=0, below plane z=40-10y and inside the…

Q: Find the volume of the region U defined by the inequalities 0≤z≤2,0≤y+z≤5,0≤x+y+z≤10.

A: Obviously, this region is a parallelopiped. It’s convenient to change variables in such a way to…

Q: Find the volume of the region defined by D = {(x, y, z): 0≤x+y≤ 1,0 ≤ y + z ≤ 2, 0≤x+z≤3}.

A: The given region is D=x,y,z : 0≤x+y≤1, 0≤y+z≤2, 0≤x+z≤3. To find: Volume of the given region. Please…

Q: Find the volume of the region bounded by y = 1 − x 2, z = 1,y = 0, and z + y = 2.

A: We know that volume V of a region W is, V=∫∫∫Wdxdydz

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…

A:

Q: If the area bounded by y = x² and y = 2 – x² is revolved about the x – axis and a vertical…

A: We have to find the volume of the solid if the area bounded by y=x2 and y=2-x2 is revolved about the…

Q: 2. Find the volume of the region bounded by y = vx and y 4x rotated about the x-axis.

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Q: 20. Find the volume of the region bounded by z = 6x/1+y³+y, z = 0, y = x, y = x/3, and y = 2.

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Q: Find the volume under z= 6x +6y and above the region bounded by y=x and x=y !!

A: Given z=6x5+6y5 bounded by region y=x2 and x=y2 Intersection points are by x=y2 we get y=xput y=x in…

Q: 30. Find the volume obtained by rotating the region bound by the graph y = e²+e-2#, x = -2, x = 3…

A: Given that the region is bounded by y=ex+e-2x,  x=-2, x=3, y=0.And the region is rotated about…

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

A: For calculating the volume of the solid revolution about particular axis, we will find the original…

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: Find the volume of the region bounded by z = +x, z = 0, y = 3x, y = x, and y = 3.

A: The region bounded by z=ey2+x, z=0, y=3x, y=x and y=3 will have the following projection in…

Q: Find the volume of the region bounded by z = 16 - y, z = y, y = x 2, and y = 8 - x 2.

A: The objective is to determine the volume of the solid that is bounded by the region z=16-y, z=y,…

Q: 4. Find the volume of the region bounded by y = -x+1, x = 0 and y = 0 revolved about the x-axis.

A:

Q: Suppose that R is the finite region bounded by y = x, y = x + 3, 0, and x 1. Find the exact value of…

A:

Q: Let M be the region in the first quadrant bounded by the graph of y = 2x + 3, the graph of y = x +…

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Q: 14 - Which of the following is the volume of the object that occurs when the region bound by the y=…

A: We sketch the region using a graphing calculator  The shaded region will rotate around the x axis

Q: Find the volume of the region satisfying x^2+y^2+z^2 ≤ 1 and z ≥ 1/2.

A: The given region is x2+y2+z2≤1 and z≥12. Find the volume of the given region.

Q: What is the volume (in πcu. units) of the region bounded by the curve y=x^3, and the lines x=1, x=2…

A:

Q: O Find volume bounded by above Z=4-x-y below Z= x4 yz

A: Given curve is z=4−x2−y2 and z=x2+y2. We have to find the volume bounded by the above z=4−x2−y2 and…

Q: Find the volume of the region bounded by y = √x and y = x rotated about x = -4.

A:

Q: A region is bounded between x = 0, y = 1, x = 1, and y = (x-1)^2+1. What is the volume generated if…

A: *to find:- generated volume about x-axis.

Q: 4. Find the volume of the region bounded by y = - x+1, x = 0 and y = 0 revolved about the x-axis.

A:

Q: The volume of the region bounded by x² + y² + z2 =1 is

A:

Q: 6. Find the volume of the region in the first octant bounded above by the cylinder z = 1- y and…

A:

Q: 6. Find the volume of a solid whose base is the region bounded by y = 4 – x² and the x-axis and…

A:

Q: 2. Find the volume of the region bounded by y = x3 and y = x rotated about %3D the x-axis.

A: In this problem we can use washer method to find the volume of the solid of revolution. Washer…

Q: What is the volume in the first octant bounded by x2 = 16 – y and z + y = 16.

A: Given curves are

Q: Determine the volume of the region enclosed by the graphs of z = f(x, y) = (x − 1)2 + y 2 and z =…

A:

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

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Q: Find the volume of the region bounded by y=x^3 and y=x rotated about the x-axis.

A:

Q: Suppose that R is the finite region bounded by f(x)=√x and f(x)=x3. Find the exact value of the…

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Q: Suppose that R is the finite region bounded by y = x, y = x + 1, x = 0, and x = 2. Find the exact…

A:

Q: 8. Find the volume generated when the plane area bounded by y=-x²-3x + 6 and x + y - 3 = 0 is…

A: Finding the volume generated by revolving along x and y axis

Q: 3. Find the volume formed by the revolving the region bounded by: f(x) = (25 – x^2)^(1/2) and g(x)=3

A: “Since you have asked multiple question, we will solve the one question for you. If you want any…

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…

A:

Q: 9) Find the volume of the region bounded by y = x + 1 x +1' Y = 0, x = 0, and у %3D0, х%3D x = 4…

A: The formula for the washer method around the x-axis is V=π∫abf(x)2-g(x)2dx where f(x) is the top…

Q: 46. Find the volume of the solid produced by rotating the region enclosed line y = -1 that is…

A:

Q: 5. Find the volume of generated by rotating the region bounded by x = 4y – y? and x = 0 (a) about…

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Q: Suppose that R is the finite region bounded by y = x, y = x + 5, x = 0, and x = = 4. Find the exact…

A: Find the required Volume of oABC

Q: Suppose that R is the finite region bounded by y = x, y = x + 1, x = 0, and x = 5. Find the exact…

A: In the Given Problem we have to find Volume bounded by  y=x , y=x+1 , x=0 and x=5 about x-axis   As…

Q: Find the volume of the region enclosed by z = 1 - y² and z = y² - 1 for 0 < x < 42. V =

A:

Q: 2. Find the volume of the region common to the cylinders r2 + y² = 9 and z2 + z² = 9.

A: USING  FORMULA VOLUME =8∫∫∫dxdydz

Q: 23. Find the volume of the solid formed by the region in the first quadrant bounded by: x = y-y3, x…

A: Consider the graph:

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: 4. Sketch the region, draw in a typical shell, identify the radius and height of the shell, and…

A: Please see the attached picture on the white board.The shaded region in the top figure is the…

Q: Find the volume of the region bounded by z = x² + y² and z = 2x

A: