and the parabola the vertical ine The region enclosed by the x-axis y=frx)=3x -x is revolving X=-1 to solid. Find the volume of the solid. Senerate

Q: y? = 8x, y = 2x; about y = 4.

A: Given that y2=8x,y=2x about y=4 . Here we have to find the volume of the solid generated by…

Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…

A:

Q: Define Q as the region in the first quadrant bounded by the line a = 6, the graph of v(y) 2y? -, and…

A:

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

A: The objective is to evaluate the volume bounded by y=2tanx, y=0, x=-π4, x=π4. Bounded region is…

Q: The region enclosed by the graphs of y = x and y = 2x is the base of a solid. For the solid, each…

A: Given:  The area enclosed by y = x2 & y = 2x is a base of the solid. The each cross-section of…

Q: The region in the first quadrant that is bounded above by the curve y = 1/Vx, on the left by the…

A:

Q: y = 3cos(x/2) the y axis and the x axis in the 1st quadrant revolved about the x-axis.

A:

Q: Find the volume of the solid with the base is the region enclosed by the parabola y = 1– x? and the…

A: Given:      Region enclosed by parabola y=1-x2 Volume of solid rotated around x-axis is given by…

Q: Find the volume of the solid that results when the region enclosed by the curves x =1 – y? and x = 9…

A:

Q: The base of a solid is the region between the line y = 4 and the parabola y = x'. The cross sections…

A: The base of the solid is the region between the line y=4 and y=x2. The cross sections are the…

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

A: The solid generated by revolving about the x-axis the region bounded by y=2 tan x, y = 0 and  x=-π4…

Q: The area bounded by the parabola ay = x², %3D the x-axis, and the line x = b is revolved about the…

A:

Q: 1. Find the area bounded by the curves y?=2ax, y²=4ax-a? 2. By integration, show that the area of a…

A: As you have asked multiple questions so I have answered first question as per the guidelines

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

A:

Q: (a) sketch the region enclosed by the curves, (b) describe the cross section perpendicularto the…

A:

Q: Find the volume of the solid that results when the region enclosed by the curves x =1- y? and x = 9+…

A:

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

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 the solid of revolution generated by revolving the region in the first quadrant…

A:

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

A:

Q: )Given the region bounded by the graphs below, find the volume of the solid generated by revolving…

A:

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

A: We can use disk and washer's method to solve this question.

Q: The area enclosed between y In (x), the x-axis and x = 3 is rotated about the line x= 3. Calculate…

A:

Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…

A:

Q: The base of a solid is the region in the first quadrant between the graph of y = x and the x-axis…

A:

Q: Find the volume of the solid of revolution generated by revolving the region in the first quadrant…

A:

Q: The region in the first quadrant that is bounded above by the curve y = 1/sqrt(x), on the left by…

A: Given,

Q: The region bounded by y = 3x - 9 andy = -3x2 + 18 x - 9 revolved about the y-axis. Find the volume…

A:

Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…

A:

Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…

A: The given curve is y=4cos x revolved about the x-axis. We have to find the volume of the solid that…

Q: Find the volume of the solid that results when the region enclosed by e8z x = 0, x = 9, and y = 0 is…

A:

Q: Find the volume of solid generated if the area bounded by each of the following curves is revolved…

A: Given Curve are y=x2,y=4,x=0

Q: Find the volume of the solid whose base is the region in quadrant I between the curve y = x' and the…

A: It is given that the cross section of squares parallel to y-axis, it means we have to cut slices of…

Q: The region in the first quadrant that is bounded above by the curve y = 1/x^(1/4), on the left by…

A: Graph the situation using graphing calculatorWe have to rotate the shaded region.

Q: Find the volume of the solid with the base is the region enclosed by the parabola y = 1 – x? and the…

A: Let's find.

Q: An area is bounded by y^2 =12x, x = 3. The area is located in the first quadrant. Calculate the…

A:

Q: The region bounded by the graph of y=Vx+2, the x-axis and the y-axis rotates about the x-axis. Find…

A:

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

A: I use washer method

Q: The region in the first quadrant enclosed by the coordinate axes, the curve y = ex, and the line x =…

A: To determine the volume of the solid of revolution about the y-axis.

Q: The region in the first quadrant bounded by the graph of y sec x, x=, and the axes is rotated 4…

A:

Q: Find the volume of the solid that results when the region enclosed by the curves x = 1 – y? and x =…

A: Here is the solution of the given:  Application of Washer Method::

Q: Find the volume of the solid that results when the region enclosed by 1 the curves y = x² and x =…

A: The volume of the solid generated by revolving about the y−axis a region between the curves x=f(y)…

Q: The region bounded by the parabola y = x and the line y =in the first quadrant are revolved about…

A:

Q: The region in the first quadrant bounded by the graph of y=8-x3/2, the x-axis, and the y-axis is…

A:

Q: (b) Find the area of the region enclosed by x = y² and y = x – 2. (c) Find the volume of the solid…

A: The formula to find the area between the regions enclosed by x=y2 and y=x-2 is given below:…

Q: An area is bounded by x^2 = 8y, y = 3, and the y-axis. This area is located in the first quadrant.…

A: An area is bounded by x2=8y, y=3, and the y‐axis. This area is located in the first quadrant.To…

Q: d the volume of the solid formed by revo

A: Given : The equation of the parabola y2 = 9x and the line y = 3x , about y - axis.

Q: - y = -a? + 6x - 8, y 0; about the y-axis

A:

Q: The region bounded by the graph of y=Vx+1, the x-axis and the y-axis rotates about the axis. Find…

A: Given query is to find the volume of the solid generated.

Q: The region in the first quadrant that is enclosed by the x-axis and the curve y = 3x√(1 - x) is…

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.