Find the volume of the solid generated by revolving the region bounded by y=Inx, y= 0 and x=e about the x-axis Select one: O e-2 O None о (е-2)п Ое-2п

Q: Find the volume of the solid generated by revolving the triangular region bounded by the lines y =…

A: a) Draw the situation first.When it rotates around x=1 then the radius = 1-xy=2x is givenSo, x=y/2

Q: Find the volume of the solid formed from revolving the region bounded by y = x2( x squared) + 4 , y…

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Q: Find the volume of the solid formed by rotating the region enclosed by x=0, x=1, y=0, y=7+x^5 About…

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

Q: Find the volume of the solid generated when the area bounded by the given curves and lines is…

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Q: Determine the volume of the solid formed by revolving the area bounded by X = 4y-y and y=X about the…

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Q: Find the volume of the solid generated by revolving the region bounded by y = x² + 2x – 2 an y = x…

A: Given regions: y=x2+2x-2 and y=x Point of intersection will be…

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

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Q: Find the volume of the solid formed by rotating the region enclosed by x = 0, x = 1, y 0, y= 4+ x°…

A: Here we have to find the volume.

Q: Find the volume of the solid generated by the revolving the region enclosed by y=(x+1)2, y=-x+5 and…

A: Given y=x+12 , y=-x+5Intersection pointx+12=-x+5⇒x2+2x+1=-x+5⇒x2+3x-4=0⇒x2+4x-x-4=0⇒x+4x-1=0∴ x=1…

Q: Find the volume of the Solid generated by revolving the region bounded by y = vx and the lines y = 1…

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Q: Find the volume of the solid generated by revolving the region enclosed by x = /30 y2, x= 0, y = -…

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Q: Find the volume of the Solid generated by revolving the region bounded by y = vx and the lines y = 1…

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Q: Find the volume of the solid generated by revolving the region bounded by y =x',y = 0, x = 2 about…

A: NOTE: Since we can solve one problem at a time, we have solved the first one. Kindly resubmit the…

Q: Find the volume of the solid generated by revolving the region bounded by y = x² + 2x – 2 and = x…

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Q: Find the volume of the solid generated by revolving about x=0 the region bounded by the given lines…

A: Solve by volume revolution

Q: Find the volume of the solid obtained by rotating the region bounded by y = 7x5, x = 3, and y = 0,…

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Q: Determine the volume of the solid obtained by rotating the region bounded by: y=3√x, x = 8 and the x…

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Q: Find the volume of solid of a revolution between y = 25-x and x+ y = 5 (smaller area) a) about y=0,…

A: Let's find.

Q: Find the volume of the solid obtained by rotating the region bounded by y = 3x², x = 2, x = 5 and y…

A: Topic- application of integration

Q: Find the volume of the solid generated by revolving the region about the y-axis. The region enclosed…

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Q: Find the volume of the solid generated by revolving the region bounded by y = √x and the lines y =1,…

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Q: Find the volume of the solid generated by revolving the region bounded by y = = the x-axis, and the…

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Q: Find the volume of the solid formed by rotating the region enclosed by y = ed" + 4, y = 0, x = 0, x…

A: Formula Used:- Volume of the solid obtained by rotating the region enclosed by y=f(x), the…

Q: Find the volume of solid generated by revolving the area bounded by : y=x^2+1, x=0, y=0 and x=2…

A: Given: y=x2+1 To find: y=0 x=2 y=5

Q: Find the volume of the solid formed by rotating the region enclosed by x = 0, x = 1, y = 0, y = 6+x6…

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Q: Find the volume of the solid generated by revolving the region bounded by y = 2x x and y = x about…

A: Given: The solid generated by revolving the region bounded by y=2x-x2 and y=x about the line x=-1.

Q: Find the volume of the solid formed by rotating the region enclosed by x = 0, x = 1, y = 0, y = 7+…

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

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

A: Hint : We can use washer method to find the required volume.

Q: Determine the volume of the solid of revolution when the region enclosed by y=x½, y = 3 and x = 0,…

A: The curves is given is y=x12 , y=3, x=0  solution: The graph for the given curve along with lines is…

Q: Find the volume of the solid obtained by rotating about the y-axis the region bounded by y=2x^2-x^3…

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Q: Find the volume of the solid formed by rotating the region enclosed by 4x y = et* + 2, y = 0, : 0, x…

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Q: Find the volume of the solid formed by rotating the region enclosed by x=0, x=1, y=0, y=5+x6 about…

A: Refer to the figure shown below:   The bounded grey region is revolved around the y-axis such that…

Q: volume of the solid generated by revolving the region bounded by y=sqrt 1-x, x=0, and y=0 about the…

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Q: Find the volume of the solid obtained by rotating the region enclosed by y=x^3, y=9x, x≥0 about the…

A: The equation of curve y=x3 , y=9x and x≥0 Washer method formula  To draw graph

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

A: The region is bounded by y=x2, y=0 and x=1 revolving about y-axis.

Q: Find the volume of the solid generated by: 3.) revolving about the x -axis, the region bounded by y…

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Q: Find the volume of the solid formed by rotating the region enclosed by x=0, x=1, y=0, y=4+x3 about…

A: Solve

Q: ind the volume of the solid formed by rotating the region enclosed by x=0, x=1, y=0, y=5+x^3 about…

A: The region enclosed by x=0,x=1,y=0,y=5+x3 about the x- axis.

Q: Find the volume of the solid obtained by rotating the region bounded by y = x and y x about the line…

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Q: Find the volume of the solid formed by rotating the region enclosed by y = est + 1, y = 0, x = 0, x…

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Q: Find the volume of the solid obtained by rotating the region bounded by y = 8x + 48, y = 0, x =…

A: shell method

Q: Find the volume of the solid obtained by rotating the region enclosed by the graphs of y = e-®, y =…

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Q: Find the volume of the solid formed by rotating the region enclosed by x = 0, x = 1, y = 0, y = 2+ x…

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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…

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Q: Find the volume of the solid generated by revolving the regions bounded by the lines and curves y =…

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Q: Find the volume of the solid obtained by rotating the region bounded by y = 2x², x = 1, and y = 0,…

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

A: The volume formula for rotating a region V=π a∫ b(r(x))2dx

Q: What is the volume of the solid generated by revolving the region bounded by y = x², y = 0 and x = 2…

A: Please see the answer below.

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.