The area bounded by y = ln x, x = e, and the x- axis is revolved about the x- axis. Find the volume generated. (use circular disk method)

Q: 2. Find the volume generated by revolving about the y-axis, the area bounded by x² + y² = a² and x+y…

A: The bounded region: Green colored    To find: The volume of revolution around y-axis of the bounded…

Q: y2- 4y + 2x = 0, x = 2 and x-axis

A:

Q: The region enclosed by the curve y = sech x, the x-axis, and the lines x = +- ln sqrt(3) is revolved…

A: Given:

Q: 10y and y = x with y > 0 X = about the y-axis. Volume

A:

Q: The area bounded by y=Inx, x=3, and the x-axis is revolved about the x-axis. Find the volume…

A: Find the volume bounded by the curves

Q: Calculate the volume y=x2   x axis,x=1 x=3 around the x axis

A: This is a simple question based on the topic application of integration which could be solved using…

Q: A/ Find the volume generated by revolving the area bounded by x = y-1 and y =5 around the x-axis?

A: We will find out the volume of solid of revolution by shell method.

Q: FIND THE VOLUME GENERATED BY REVOLVING THE AREA BOUNDED BY THE GIVEN CURVES AND LINES

A: Given curves equation is x2-y2=9 ⇒ x2=y2+9 ⇒ x=y2+9   ⇒ fy=y2+9  and line equation is  y=2x-6    ⇒…

Q: Fint the volume generated by revolving the area bounded by y= x^2 + 1, x=0, x=2 about y=5

A: Given curve is y=x2 +1 x is bounded between 0 and 2. Rotation is done about y=5. The objective is to…

Q: Find the volume generated by rotating the region in the first quadrant bounded by y=e^x and the…

A:

Q: 27. Find the volume generated by rotating the area bounded by y = x² + x, x = 1, x = 4, and the…

A: Given that: y=x2+x,   x=1,  x=4   and   the   x-axis To sketch the graph,

Q: what is the volume generated if the area bounded by the cirves x2 =8y , x=4 and y= 0 is resolved…

A:

Q: y = 3x - x2 and y = 2x 11 %3D

A:

Q: Find the volume generated by revolving the area bounded by y=ex, x=0 and y=0 about the y-axis.

A:

Q: . THe area enclased by the loop of the curved y= x (x - 3)° is Find the volume generated . revolved…

A: Here 1st we will find points where loop is formed and then shade the region bounded ,  To form the…

Q: The area enclosed by the curve x² + y² = 25 is revolved about the line x - 10 = 0. Find the volume…

A: We have to find the volume generated, in cu. units when the area enclosed by the curve x² + y² = 25…

Q: 5. Find the volume of the solid generated by revolving about y axis, the area bounded the y=(x²-4)²…

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: Find the volume generated by revolving the region enclosed by x -y and y=x+2 about у-аxis.

A: We have to find the volume.

Q: Find the volume obtained by rotating f(x) = x(1 – x) around the x-axis.

A: Given             f(x)=x(1-x) and y=0

Q: 4. Compute the volume rotating the area shown through one revolution about the x-axis. generated by

A:

Q: the area bounded by the parabola ay= x², the x-axis, and the line x= b is revolved about the x-axis.…

A: Value of 'a' may be positive or negative, taking |b| as absolute value of b.

Q: Find the volume of revolution from the region bounded by y=x, x+y=6 and y=1, being revolved around…

A:

Q: The area bounded by the parabola ay = x², the x-axis, and the line x = b is revolved about the…

A:

Q: 3. Find the volume of a sphere with radius r by integration.

A:

Q: Find the volume generated by rotating the area bounded by each set of equations around the x-axis.…

A: The volume for solid of revolution for a curve is the volume of object determined by a curve fx…

Q: om

A: Computing the volume generated by rotating the area through one revolution about the x-axis.…

Q: Determine the volume obtained by rotating the area enclosed by y = x(4 – x) and y 0 about the line x…

A:

Q: Find the volume generated when the area bounded by the two curves of x^2 = 4y and y^2 = 4x is…

A: We will find out volume of solid of revolution.

Q: Fint the volume generated by revolving the area bounded by y= x^2 + 1, x=0, x=2 about y=0

A: Here we have to find the volume generated by revolving the area about x axis .

Q: Find the volume generated by rotating the region bounded by y = x, x = 1, and y2 = 4x, about the…

A: Here we solve the integral problem.

Q: 1. Find the volume generated by revolving about x=1, the area bounded by y = (x²-₁)² and the x-axis.…

A: We have to find the volume generated by the given function.

Q: Find the volume generated by revolving about the y-axis the area bounded by the curve x2 = 4(x-y),…

A:

Q: The area enclosed by y = 4x - x^2 and 2y = 2x + x^2 is revolved about the line x = -1. Using a…

A:

Q: Determine the volume generated about y = 4, the area bounded by x + y = x? %3D and x? + y = 3.

A: To find the find the volume about y =4 Given x + y = x^2 , x^2 +y = 3

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

A:

Q: Determine the volume of the solid formed by revolving the area bounded by Y- = 4ax_and x= a around…

A: The area is bounded by the curves y2=4ax and x=a around x=9.1

Q: Find the volume if bounded region is rotated around x-axis. Give an exact simplified answer. xY = 2…

A: Givenxy=2y=3-xTo find the volume of the solid first define the area then integrate Across the range…

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

A:

Q: The area bounded by the curve y = e−x, the axes, and the line x = 2 is revolved around ox. Find the…

A:

Q: Find the volume rotated about the x-axis

A: Formula

Q: Find the volume if bounded region is rotated around x-axis. Give an exact simplified answer. y = x³…

A: We have to find the volume of the solid around x axis.

Q: Find the Volume generated by revolving the area bounded by the given curves and lines revolved about…

A:

Q: Find the volume generated by revolving about the y-axis, the area bounded by x² + y² = a² and x+y =…

A: To find the volume of solid which is generated by  x2+y2=a2 and x+y=a when revolved around y-axis.

Q: Find the volume generated by revolving about the x – axis the area bounded by y^2=4x and x^2=4y

A: The volume generated by revolving the area bounded by the curves fx and gx is V=∫abπfx2−gx2dx. The…

Q: FIND THE VOLUME BOUNDED BY THE GIVEN CURVES, sketch the graph Within x^2 − y^2 = 16, y = 0, x = 8…

A: This question is based on application of integration.

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

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.