Find the volume of the solid obtained by rotating the regic y = e-*, y = 1- e-*, and x = 0 about the line y = 4.

Q: Find the volume of solid generated by revolving the area bounded by y³=x, y=2 and x=0 about the…

A:

Q: Find the volume of the solid bounded by y = x² +1 and the line y = -x + 3, revolved about the line y…

A: Given curve y = x2 and line y = -x +3

Q: Find the volume of the solid obtained by rotating the region bounded by y= 54x-6x2 and y= 0 about…

A: Given:           y=54x−6x2 and y=0  about y−axis.

Q: Find the volume of the solid of revolution formed by revolving the region bounded by y = f(x) = 2x -…

A: The  given curve is y=2x-x2. The region is bounded by the given curve, the x-axis. The objective is…

Q: Find the volume of the solid generated by revolving the regionbounded by y = √x and the lines y = 2…

A:

Q: Compute the volume of the solid obtained by revolving the graph of y =1+x^2/2 on [0,1] about the…

A:

Q: what is the volume of a solid of revolution when the region bounded by y=x2, y=-2x-1, y=0 is…

A:

Q: Find the volume of the solid obtained by rotating the curve y=x^2 , y= square root x , the lines x=0…

A:

Q: Find the volume of the solid generated by revolving the region between y = 4 – x2 and y = -x + 2…

A: The given regions are, y=4-x2 and y=-x+2 and the given line is, x=44-x=0 We can write the given…

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

A:

Q: Find the volume of the solid obtained by rotating the region bounded by y = 54x – 6x and y = 0 about…

A: Given:y=54x-6x2  and y=0Vx=∫ab 2πx fx dx

Q: Find the volume of the solid obtained by rotating the region bounded by y=7x^2, x=1, and y=0,…

A: Given:-     y=7x2                   x=1                   y=0         about x‐axis. ∴volume v=∫ab…

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

A:

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

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 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 about the x-axis the region by y= x' and the lines…

A:

Q: Find the volume of the solid generated by revolving the region bounded by the line y = 0 and curve y…

A:

Q: Find the volume of the solid generated by revolving about the line x = 2, the area bounded by y =…

A: The equation of the curves are  C1: y = x2C2: x= 2C3: y = 0 The axis of the revolution is x = 2 To…

Q: Find the volume of the solid generated by revolving the region between the parabola x=y^2+1 and the…

A:

Q: Find the volume of the solid formed by rotating the area bounded by y = 1 the x- x+1 and y-axes, and…

A:

Q: Find the volume of the solid obtained when the region bounded by the x-axis, the y-axis, and the…

A: We have to find volume of the solid bounded by given region

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

A: We need some modification I'm original formula to solve this problem. Let's see what modification we…

Q: . Find the volume of the solid generated by revolving the region bounded by y = vx-1, y = 0 and the…

A:

Q: CALCULATE THE VOLUME OF THE SOLID OBTAINED BY ROTATING THE REGION BY 4y=x² - 4x + 8 AND THE LINES…

A: Introduction: When the axis of revolution is the plane region's boundary and the cross-sectional…

Q: Find the volume of the solid of revolution bounded by the cirde x+y = 16, and the lines z = 0 and 8,…

A: Given curve is x2+y2=16 and line x=0 and x=8 about x-axis We have to find the volume of the solid of…

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A: The region to be rotated and the limits will be as follows.

Q: Find the volume of the solid obtained by rotating the region bounded by  y = 35x − 7x2  about the…

A:

Q: Find the volume of the solid obtained by revolving the region bounded by: ソ=x ソ=4 about the line X=4

A:

Q: Find the volume of the solid obtained by rotating the region bounded by y=x^3, y=8, and x=0 about…

A:

Q: Determine the volume of the solid obtained by rotating the region bounded by y = 2vx – 1 and y =x-1…

A:

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

A: Given

Q: Find the volume of the solid obtained by revolving the region bounded by y = x², y = (x – 6)², and…

A:

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

A:

Q: find the volume of the solid obtained by revolving the region bounded by y = x - x2 and the x - axis…

A:

Q: Find the volume of the solid obtained by rotating the region bounded by y = 4x², x = 1, and y = 0,…

A:

Q: Find the volume of the solid formed by rotating the region enclosed by 5x Y = e + 4, y 0, 0, = 0.9 ,…

A:

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

A:

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

A: Given that a solid generated by the revolving the region bounded by y= √x, y=2 and x= 0 about the…

Q: Find the volume of the solid obtained by rotating the region bounded by x = 8 – y² - and x 2y about…

A: Given the region is bounded by the curves x=2y and x=8-y2 about the line x=9. The curves intersect…

Q: Find the volume of the solid generated by revolving the specified region about the given line. R…

A: Find your answer below

Q: Find the volume of the solid generated by revolving the region bounded by y = 8x - x and y = x about…

A: Given curves are                                              y=8x-x2y=x…

Q: Find the volume of solid formed by revolving region by f(x)=x^(2/3), x=0, y=0, y=1 about the y-axis.

A: Given:

Q: Find the volume of the solid obtained when the region bounded by the line y = 2x, the line x = 3,…

A:

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

A: The region bounded by the curves y=x2-2x and y=x about the line y=4 is as shown above.

Q: Find the volume of the solid formed by rotating the region bounded by y = x² + 3, x = 0, x = 2, and…

A: The solid is formed by rotating the region y=x2+3, x=0, x=2 and y=0about the x-axis

Q: Find the volume of the solid generated by revolving the regionbounded by y = √x and the lines y = 2…

A: The curve given is  y = √x and the lines y = 2 and x = 0 about the line y = 2. The graph of the…

Q: Find the volume of the solid generated by revolving the region bounded by y = 3x – x² and y x2 about…

A:

Q: Find the volume of the solid obtained by rotating the region bounded by y-2vx-1 and y=x-1 about the…

A:

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

A:

Q: Find the volume of the solid generated by revolving the regionbounded by y = √x and the lines y = 2…

A: To find the volume of the solid generated by revolving the region bounded by  y=x and the lines y=2…

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.