b) Find the volume generated by revolving the region enclosed between y = -2x, x = -3, and x – axis around y = 6 (Sketch the region)

Q: 1. Use cylindrical shells to find the volume of the solid generated when the shaded region is…

A:

Q: By Sketching the graph, find the volume of the solid generated by revolving the region given by, 9 –…

A: The volume of the solid formed by revolving the region bounded by the curve and the y-axis between…

Q: Find the volume of the solid generated by revolving the region enclosed by the triangle with…

A: If  you like the solution then please give it a thumbs up.. The Answer is:     Volume = 4π3

Q: 5. Find the volume of the solid generated by revolving the area of a circle: (x - 2)² + y² = 4;…

A: In this question, we need to find the volume of solid generated by revolving the area of the given…

Q: By Sketching the graph, find the volume of the solid generated by revolving the region given by, y =…

A:

Q: Find the volume of solid generated by revolving te area enclosed by : x=y²+1, x=0,y=0 and y=2 about:

A:

Q: a) Find the volume and the lateral surface area of the solid formed by rotating this func- tion…

A:

Q: 3. Find the volume generated by revolving the area bounded by the parabola y² = 8x and its latus…

A: Given

Q: 3. Use cylindrical shells to find the volume of the solid eenerated when the shaded region is…

A:

Q: 4. Find the volume of the solid that results when the shaded region is revolved about the indicated…

A: Solution... We have volume of solid obtained by rotating the shaded region about x-axis. let…

Q: Find the volume formed by rotating about the y-axis the region enclosed by: 11y and y = x with y>0

A: Given the equation of curves which region formed is rotating about y−axisx=11yy3=x

Q: Find the volume of the solid generated by revolving the region enclosed by the triangle with…

A:

Q: b) use cylindrical shell to find the volume of the solid generated when the region under y= x , y=…

A:

Q: Use the Theorem of Pappus to find the volume of the solid of revolution The torus formed by…

A:

Q: Find the volume generated by revolving the area 1 bounded by y 3, x = 4, and y = 0 about the y-axis…

A: Solution

Q: A. Detemine the volume of the solid generated by revolving the region bounded by the graphs of the…

A: use formula

Q: Find the volume of the solid formed by revolving the re-gion bounded by the graphs of y = sin x +…

A: The given graph of the functions are

Q: Sketch the region bounded by the curves: y = e*,y = Inx, x = 1 and x = 2, then find, the area of…

A:

Q: 4. Determine the volume of the solid obtained by rotating the portion of the region bounded by y =…

A:

Q: ) Find the volume formed by rotating the region enclosed by: x = 3y and y = x with y > 0 about the…

A:

Q: 1- Find the volume of the solid generated be revolving the shaded region about the given axis. About…

A: The volume of the solid generated when the first given region is revolved around the y-axis is to be…

Q: Find the volume generated by revolving the area 1 bounded by y = 2, x = 5, and y = 0 about the…

A: Given that to find the volume generated by revolving the area bounded by  y=1x3+17x2+72x,  x=2,…

Q: Determine the volume of the solid obtained by rotating the portion of the region bounded by…

A: First we have to plot the given region.

Q: Find the volume formed by rotating the region enclosed by: 6.2y and y° = x with y > 0 about the…

A:

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: Derive the formula for the volume of a right circular cone of height h and radius r using an…

A: Given information:

Q: b) Determine the volume of the solid generated by rotating the region bounded by y = V2x and y =…

A: We have given the curves

Q: 4- Find the volume of the solid generated by revolving the region about y-axis,the region in the…

A: Draw the graphs of y=x2, x=2 and identify the region bounded by the curves. The required region is…

Q: Find the volume of the solid generated by revolving the region enclosed by the triangle whose…

A:

Q: B. Find the volume generated by revolving the region enclosed by x - -y and y=x+2 about У-аxis. 20%

A:

Q: Find the volume formed by rotating the region enclosed by: 5y and y = x with y > 0 about the y-axis…

A: Given Data The first equation is x=5y. The second equation is y3=x.   Equate the given both…

Q: Find the volume of the solid generated by revolving the shaded region about the given axis. About…

A: When x=5 then  x=y255=y25y2=25y=5 So y is from 0 to 5 in the figure.

Q: Find an expression for the volume of the solid of revolution obtained by rotating the region in the…

A:

Q: 2. y = x2, y = x³ , revolved at y axis

A:

Q: Find the volume generated by revolving the plane area generated by the equations y = ex^2, y=0, and…

A: To find the volume of solid formed when the region bounded by y=e-x2, y=0 and  x=0  about the…

Q: 1. Use cylindrical shells to find the volume of the solid generated when the shaded region is…

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

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: 15. Find the volume of the solid generated by revolving y-axis, the area enclosed

A:

Q: Use the Theorem of Pappus to find the volume of the solid of revolution The solid formed by…

A: Theorem of Pappus: The volume of solid of revolution generated by revolving a lamina about an axis…

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

A:

Q: (4) Find the volume of the solid obtained by rotating the region bounded by y = r, y = 0, x = about…

A: Given:- y=x3,  y =0 and x=1 To find:- Volume of solid about line x=2

Q: 5. y = 4x – x², x = 0 , y = 4 , revolved at y axis -

A:

Q: By Sketching the graph, find the volume of the solid generated by revolving the region given by, y =…

A:

Q: A. Find the volume generated by revolving the region enclosed by y = 4Vx, y = %3D 2-x and y =x +3…

A:

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

A: In this question we have to just find the volume generated by rotation.

Q: (b) Use Disc method to find the volume of the solid formed by revolving the region bounded by f(x) =…

A: Integrals and derivatives are considered as inverses of each other. For example if we have a…

Q: By Sketching the graph, find the volume of the solid generated by revolving the region given by, y =…

A:

Q: Find the volume of the solid generated by revolving the shaded region about the given axis.

A: We need to find volume.

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

A: The volume of the region bounded by the curves y1(x) and y2(x) is given by the formula…

Q: Find the volume of the solid generated by revolving the region enclosed by y=x3, y=8 and x=0 about…

A:

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.