Find the volume of the region under the surface z = 9x and above the triangle in the xy-plane with corners (0, 0, 0), (5, 0, 0) and (0, 3, 0).

Q: Find the volume of the solid generated by the region bounded by y - x² = -3,x+y = 3 about y = -5.

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Q: Find the volume of the solid of revolution formed by rotating about the x-axis each region bounded…

A: Given equations are ƒ(x) = x2, y = 0, x = 1, x = 5. Graph the given region as shown below.

Q: Find the volume of the solid generated of the area bounded by y = x², y + 2x = 8 and y = 0, rotated…

A: This question can be solved by first plotting the graphs to get the feel of the area enclosed.

Q: Find the volume of the region above the xy-plane, inside the cone z = 18 – Vx² + y² and inside the…

A: We have to find the volume of the region bounded by the xy-plane, inside the cone, and inside the…

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

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Q: Find the volume of solid lying in the first octant bounded by the graphs of : z = 4 – x2 – y² , y =…

A: The volume of the solid in first quadrant is given by: V=∫ab∫cdf(z)dydx Now, find the range of the…

Q: Use an appropriate change of variables to find the volume of solid region lying below the surface…

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Q: Find the volume of the solid of revolution formed by rotating each bounded region about the…

A: The volume of Revolution about x -axis is given by  V = ∫x=ax =b π y2 dx  Given,  y = x32  x = 4 and…

Q: Find the volume of the solid formed by rotating the region enclosed by у 3 е + 5, у — 0, х — 0, х —…

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Q: Find the volume of the solid of revolution formed by rotating about the x-axis each region bounded…

A: given fx=3x , y=0, x=0 ,x=2

Q: Find the volume of the solid obtained by rotating the region bounded by y = x^3 , y = 0 and x = 1…

A:

Q: Find the volume of the region under the surface z = 6x° and above the triangle in the xy-plane with…

A:

Q: Find the volume of the solid of revolution formed by rotating about the x-axis the region bounded by…

A: Solution: Consider the given equations are y = x + 1 y = 0 x = 1 and  x = 4 If we construct bounded…

Q: Find the volume above the xy-plane bounded by the surfaces: 3 2a ²+y² = a², z =y and z= 0. Ans.

A: Given,

Q: Find the volume of the solid obtained by rotating the region bounded by y = x² + 2 and y = 4 - x²…

A: Solution:-

Q: Find the volume of the region under the surface z = corners (0, 0, 0), (6, 0, 0) and (0, 3, 0). 824…

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Q: Find the volume of the region under the surface z and above the triangle in the xy-plane with 1+ x²…

A: We have to find the volume of the region under the surface.

Q: Find the volume of the solid that is bounded above by the cylinderz = x2 and below by the region…

A: Given, bounded region z=x2, y=2-x2, y=x region can be define as ∫∫x2dxdy now region is y=2-x2, y=x…

Q: Find the volume of the solid of revolution formed by rotating the bounded region about the x-axis.…

A: Consider the solid formed by the following curve. fx=4-x2,  y=0, x=-1 and x=1   Volume of the solid…

Q: Find the volume of the solid obtained by rotating the region bounded by y = 6x², x = 2, x = 5 and y…

A: Use formula about x axis

Q: Find the volume of the solid generated by the region bounded by x² + y = 6, y = x, y = -2 and x = -2…

A: Follow the steps.

Q: Find the volume of the region under the surface z = 4x* and above the triangle in the xy-plane with…

A: The solution follows as

Q: Find the volume of the solid below the surface z = xy and above the triangle in the xy-plane bounded…

A: Find the region R in the x-y plane.The x-axis is y = 0 and y axis is x = 0 line.From the graph the…

Q: Find the volume of the region under the surface z = and above the triangle in the xy-plane with 1+…

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Q: Determine the volume of the solid of revolution which is formed when the area bounded by x = -4.5, x…

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Q: Find the volume of the solid bounded from up by surface f (x,y) = 2x + y2 and from below by the…

A: According to question, surface :f(x, y) = 2x+ y2,Traingle vertices : 0, 2, 0, 0 and 3, 2

Q: Find the volume of the solid bounded by x + y2 = 3z and x2 + y2 = 6x

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Q: Find the volume of the solid with the order dzdydx bounded by x2  + y2  = 4 and the planes x + z=2,…

A:

Q: Find the volume of the solid obtained by rotating the region bounded by y = 7x², x = = 1, and y = 0,…

A:

Q: Find the volume of the solid of revolution formed by rotating about the x-axis each region bounded…

A: Given that : The curves f(x) = 3x , y = 0, x = 0 and x = 2.

Q: find the volume,The region bounded in back by the plane x = 0, on the front and sides by the…

A: Given

Q: Determine the volume of the solid obtained by rotating the region bounded by y= 2x2 and y = x³ about…

A: Let's find.

Q: Find the volume of the solid bounded above by paraboloid z=4-x^2-y^2 and below by region bounded by…

A: According to the given information, it is required to find the volume of the solid bounded by the…

Q: Find the volume of the solid of revolution formed by rotating about the x-axis each region bounded…

A: Given that the region is bounded by y=x2,  y=0,  x=1  and x=5. Sketch the region as shown below.

Q: Find the volume of the region under the surface z = and above the triangle in the xy-plane with 1+x2…

A:

Q: Find the volume of the solid bounded above by the surface z = 4 – y² and below by the rectangle R =…

A: We have to find the volume of the solid bounded above by the surface z= 4 - y2 and below by the…

Q: Find the volume of the region above the triangle with vertices (1,0), (0,1) and (3,1), below the…

A: Given Data: fx,y=x2y The vertices of the triangles are (1,0), (0,1) and (3,1).

Q: Find the volume of the solid obtained by rotating the region bounded by y = x² + 2 and y = 4 - x²…

A:

Q: Determine the volume of the solid obtained by rotating the region bounded by y= 2x2 and y = x³ about…

A:

Q: Find the volume of the solid bounded above by the cylinder y = x2 and below by the region enclosed…

A:

Q: Find the volume of the region bounded above by the elliptical paraboloid z = 16 - x2 - y2 and below…

A:

Q: find the volume of the region in the first octane bounded by the coordinant planes, the plane y + z…

A: See the details solution in below

Q: Find the volume of the solid bounded by x+y2=3z and x2+y2=6x.

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

A: Solution of given question is written in below steps.

Q: Determine the volume of the solid obtained by rotating the region bounded by y = 2x + 1, y = 3 and x…

A:

Q: Find the volume of the solid capped by the surface z = 1 – y – x² over the region bounded on the xy-…

A: To find the volume of the solid capped by the surface z = 1 - y - x2 over the region bounded on…

Q: Find the volume of the region in the first octant bounded by the coordinate planes, the plane x + y…

A:

Q: Find the volume of the solid in the first octant bounded by the parabolic cylinder z= 25 - x and the…

A: Since we are considering only in the first octant so lower limit of both x and y will be zero.…