Find the volume of the region bounded by z = x2,0

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

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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: Find the volume bounded by the function z = f(x, y) = xy√x² - y² 8≤x≤10 and 0≤ y ≤8. over the…

A: Volume bounded by a function z=f(x,y) and a region R=x,y:a≤x≤b,c≤y≤d is given by V=∫ab∫cdzdydx

Q: Find the volume obtained by rotating the bounded region defined by y = Vx y = 0 , and x = 4 around…

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Q: Find the exact value of the volume of the solid obtained by rotating the region bounded by y = Va, x…

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Q: Determine the volume V of the region bounded by z=x²+y², z=2x²+2y², y=x, and y=x².

A: Volume is a scalar quantity expressing the amount of three-dimensional space enclosed by a closed…

Q: Find the volume of the region between the planes x+y + 2z =2 and 2x + 2y +z = 4 in the first octant.

A: Find the volume of the region between the planes  x +y + 2z = 2 ......... (1)  and  2x + 2y +z =4…

Q: Find the volume of the solid formed by revolving the region bounded by the graphs of y = x2 + 1, y =…

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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: Find the exact value of the volume of the solid obtained by rotating the region bounded by y = VT, x…

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Q: Find the volume of the region enclosed by the cylinder x2 + y2 = 4 and the planes z = 0 and x + y +…

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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 enclosed by the cylinder x2 + y2 = 4 and the planes z = 0 and y + z =…

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

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Q: Find the volume of the region bounded by the cylinder x^2 + y^2 = 2y and the planes z = 0 and x + y…

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Q: What is the volume of the region bounded by the lines f (x) = x²,x = 2, and y 49 rotated about the…

A: Given data:     The given equation is: f(x)=x2. The second equation is: x=2. The third equation is:…

Q: Find the volume of the region en-closed by the cylinder x2 + y2 = 4 and the planes z = 0 and x + y +…

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Q: Consider the region enclosed by y=x2 , the y-axis, and y=1. Set up the integral of the volume of the…

A: Here is the solution of the given problem:  Washers Method:  Cylindrical Method::

Q: 4.Find the volume of the solid that is obtained by rotating the region bounded by y = /x +1, y = Vx…

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Q: Find the volume of the solid that results when the region bounded by y = Vā ,y = 0 and æ = 4 is…

A: Volume

Q: Find the volume generated by rotating the region bounded by y = x, x = 1, and y? = 4x, about the…

A: Given curves are y=x, x=1   and  y2=4x We have to calculate the volume generated by these curves…

Q: Find the volume of the solid obtained by rotating the region bounded by y = x3, y = 0, and x = 2…

A: Follow the steps.

Q: Find the volume generated by rotating the area bounded by y = ,* = 2, x = 7, and y = 0 about the y…

A: The solid obtained by rotating the region between the grah of fx and the x-axis from x=a to x=b…

Q: Find the volume generated by revolving the area bounded by xy=4, x=1, x=4 and the x-axis about the…

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

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Q: Find the volume in the first octant bounded by the cylinder x² +y = a² 2a and the lane z = x + v.

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Q: Find the volume bounded by the function z=f(x,y)=xy√√x² - y² over the rectangular region 8≤x≤10 and…

A: Volume bounded bya function z=f(x,y) and a region R is given byV=∬Rfx,ydydx

Q: Find the volume of the solid whose base is the region enclosed by y=x^2 and y=4, and the cross…

A: Given: Region enclosed by y=x^2 and y=4. And the cross sections perpendicular to the y-axis are…

Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the cu…

A: We have to find volume

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

A: To find the volume of the region enclosed by z=1-y2 and z=y2-1 for 0≤x≤42

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

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Q: find the volume,The finite region bounded by the planes z = x, x + z = 8, z = y, y = 8, and z = 0

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Q: Find 5x dA over the region R = {(x, y) | 0 < x < 2,0 < y < 6} by identifying it as the volume R of a…

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Q: find the volume generated by rotating the region bounded by the curves x = Vỹ, x = 0, and y = 8…

A: given curves are x=y, x=0 and y=8 find the volume

Q: Find the volume of the solid whose base is the region in the first quadrant bounded by y=x^5, y=x,…

A: The solid base is in the first quadrant which is bounded by the curves y=x5, y=x, y=1 and y-axis.…

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

A: The graph is where red curve represents y=x and blue line represents y=x.

Q: Find the volume of the solid obtained by rotating the region bounded by y=x^4 and y=1 with 0 being…

A: We have given

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

A: Given that the region in the first octant bounded by the coordinate planes, the plane y+z=2 and the…

Q: Find the volume of the solid that results when the region bounded by v-x1=0 and x=l04 is revolved…

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

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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 region bounded by z = x²,0 ≤ x ≤ 5, and the planes y = 0, y = 2, and z = 0.…

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Q: Find the volume of the solid obtained by rotating about the x-axis and the region bounded between: y…

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Q: Find the volume of the solid that results when the region bounded by y = x and y = x², from x = 0 to…

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Q: Find 3dA over the region R {(x, y) | 0 < x < 5,0 < y < 6} by indentifying it as the volume of a…

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Q: Find the volume of the solid under z=4x and above the region bounded by y=x2 , y=4, and x=0

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

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.