QUESTION 3 Let R be the region bounded by xr=y², x= 0 and y=2, then the volume of the solid formed by revolving R about the y - axis is ST (y')² dy V= V= п (у)' dy S'n (2-/x)°dr V= x)*dr 0. попе

Q: 8. Suppose you revolve the region completely about the of revolution. Describe the solid and find…

A: Introduction: A stable of revolution is a stable determine created via way of means of rotating a…

Q: 2. Sketch the region R enclosed by the triangle with vertices (1,0), (2, 1) and (1,1) and find the…

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Q: The region R is bounded by the curve y = x² +3, x = -1, x = 2 and y = 1. Find volume of the solid…

A: The given curve is, y=x2+3, x=-1, x=2, y=1

Q: (5) Use Wolframalpha to find the exact volume of the solid obtained by rotating about sinx, x =…

A: Given,              y=sin2x,  y=sin4x, x∈0, π2   about x=π2.

Q: 3. SET UP ONLY: Find the volume of the solid of revolution generated by revolving the shaded region…

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Q: The region bounded by the given curves is rotated about the specified axis. Find the volume V of the…

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Q: 1. Find the area of the region bounded by the graphs of the equation y = x and y = x?. 2. Find the…

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Q: Let R be the region bounded by the following curves. Find the volume of the solid generated when R…

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Q: 4. The curve represented by y = x? from (0, 0) to (1, 1) is rotated about the x-axis, what is the…

A: Let us consider the 5th question 5.

Q: 3. Find the volume of the solid form by the region bounded by the curves y = =,y = 2-x is revolved…

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Q: The region bounded by f(x) = -7 sin a, a = T, a = 2T, and y = 0 is rotated about the y-axis. %3D %3D…

A: According to the given information, it is required to find the volume of the solid of revolution.

Q: Find the volume V obtained by rotating the region bounded by the curves about the given axis. y = 2…

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Q: Find the volume V obtained by rotating the region bounded by the curves about the given axis. y = 5…

A: Graph the situation first The shaded area is rotating about the y=-5 line.

Q: about the line y = -3 4 Find the volume of the solid obtained by rotating the region bounded by the…

A: Curves y=4sinx              y=4cosx

Q: a. Sketch and shade the region bounded by the graphs of 2x + y = 2 and x + 2y = 4 and y = 0, and…

A: using washer method

Q: Suppose you revolve the region completely about the line y-3 to sweep out a solic of revolution.…

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Q: 2. Find the volume of the solid obtained by rotating the curve x = 1+ (y – 2)² about the x-axis. The…

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

Q: A solid is generated by revolving about the x-axis the region bounded by the graph of the positive…

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Q: 2. Sketch the region R enclosed by the triangle with vertices (1,0), (2, 1) and (1,1) and find the…

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Q: 1. Find the volume generated by revolving about the x-axis the area bounded by the lines y 2x + 1, y…

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Q: An area R is limited by y = x3 + 1, the line y = 0 and between x = 0 and x = 2, calculate the volume…

A: Volume  can be defined as below:

Q: a. Sketch and shade the region bounded by the graphs of 2x +y = 2 and x + 2y = 4 and y = 0, and…

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Q: 1. Find the area of the region bounded from the right by the curve x = 4 – y? , from the left by the…

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Q: The region bounded by the given curves is rotated about y = 7 x = (y – 9), x = 4 Find the volume V…

A: and the vertical line is  make a rough sketch

Q: 2. Show the volume of the solid obtained by rotating about the x-axis the region 1 under the curve…

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Q: 1. The region bounded by the curves y =7x and y=x² is rotated about the x-axis. USE THE METHOD OF…

A: Two given curves are  y=7x  (i)y=x2  (ii) The region bounded by these two curves is R and R is…

Q: 7) Consider the region bound by y=e", y=1, x 0, x= 2 a) Set up the integral for the volume if the…

A: a) We sketch the region using a graphing calculator  The shaded region is rotating about the x-axis…

Q: The region R in the first quadrant of the xy-plane is bounded by the graphs of y = 1 + x² and y = 1,…

A: Sketch the region and use shell method

Q: If the region under the graph of 1 x² y = x² + from x = 1 to x then the volume of the resulting…

A: The objective of the question is determine the volume and choose the correct option.

Q: 1. y = 3x - x² and y = 3-x Find the volume of the solid generated by revolving about the line x = 4…

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Q: Question 4. The region bounded by the curve ry = 5 and the line y = -1 +6 is revolved about the line…

A: The objective is to compute the volume of solid by using the disk method and method of cylindrical…

Q: Find the volume of the three-dimensional body caused by rotating a given straight line around an…

A: As per Bartleby's answering policy, we can answer only one question, so kindly post the remaining…

Q: Consider the region R bounded by the curves y = ln(x)+1, y = –x+2, and the vertical line 5. (The…

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Q: 4. Find the volume of the solid generated by revolving about the line y=-3 the region bounded by the…

A: Using disc method, volume is evaluated.

Q: EXAMPLE 3 The region bounded by the curve y = Vx, the x-axis, and the line x = 4 is revolved about…

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Q: Let R be the region bounded by the graph of y = 5Vx+3, the a-axis, the y-axis, and the line x = 4.…

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Q: 3. The line y = x + 2 and the parabola y = x contain a bounded region R between them. Find the…

A: Given, the line y=x+2 and y=x2

Q: The region bounded by the given curves is rotated about the specified axis. Find the volume V of the…

A: Given Curves are

Q: 1. Consider the region bounded by y = 5 - x 2, y = x - 1, and x = 1. Find the volume of the solid…

A: Consider the equation

Q: The triangular region with corners (6,0), (7,0) and (7,3) is rotated about the line x = –1. The…

A: Given - Vertices of triangle and volume of solid  To Find - Constant in the expression of volume

Q: 4. The region bounded by the parabola y = x² and the line y = 2x in the first quadrant is revolved…

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Q: 3. Region R is bounded by the given curves. Set up the integral of the volume V(R) of the solid…

A: The volume of a region rotated about an axis other than the x-axis or y-axis can be found by the…

Q: 5. Find the volume of the solids generated by revolving the regions bounded by the curve y = sec y =…

A: Here, the region bounded by the curve y=sec x, y=0  from x=-π4 to x=π4 about x-axis is:

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

A: According to question given:y2-x=2, y=x Is revolved about x=2We have to calculate the volume.

Q: 9. Find the volume of the solid of revolution formed by rotating about the x-axis the region bounded…

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Q: 1) The region R in the first quadrant is bounded from above by y=2+- and below the x-axis, between…

A: The required region is as follows:

Q: 9. The region enclosed by the x-axis, the curve y= Vx and the line x=3 is rotated around the x-axis.…

A: Given y=0,y=x,x=3Rotation about x axis at y=0⇒x=0So here,X varies 0 to 3

Q: b) […. obtained curve 1: Find the volume of the solid by rotating the region bounded by the y = -x²…

A: Given :y=-x2+9y=x2+1

Q: 1. Sketch and shade the region bounded by the curves x y2 and x +y 2. Find the volume of the solid…

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.