1-4 Find the area of the surface generated by revolving the given curve about the x-axis. 2. y = , 1sx <4

Q: 7. Let C be the curve y = 3x for 0 <x S 1. 0.5 Find the surface area of revolution of C about the…

A: Given: y=3x3 for 0≤x≤1

Q: 3. Find the area of the surface generated by revolving about the y-axis the part of the curve y = x?…

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Q: x In(x) 5. Find surface area generated when the curve y =- 4 for 1<x<2 is rotated about the 2…

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Q: 9. r= 4 cos 0

A: According to question given that r=4 cosθ

Q: Find the area between the curve y = cos (2x) and the line joining the points (pi/4, 0) and (pi/6,…

A: Area of the region is (2-√3)/4

Q: 1. Find the area of the region bounded by the parabola x = 3 + 2y – y? and the line 2x + 3y = 6.

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Q: 20. Find the area of the region bounded by the curver=8 cos 20. С. 12л A. 16π В. 32л D. 8t

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: 12. Find the area of the region enclosed between the curves defined by the equations y = √(x + 2), y…

A: We have to evaluate the area of the region bounded by the curve y=x+2 and the line y=x using the…

Q: 2. Find the area of the region that lies inside both curves r = 4 sin(0) and r = 4 cos(0) ● 플 +1 2T…

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Q: 6. Determine the volume V of the 3 dimensional lampshade formed (see diagram below) by rotating the…

A:

Q: The circle of radius 3 centered at the origin Ex. to calculate the area of the given region.

A: Given: The region between x-axis and the cycloid parametrized byr(t)=t-sin t, 1-cos t  for 0≤t≤2π

Q: Find the exact area of the surface obtained by rotating the given curve about the x-axis. x = a cosº…

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Q: Find the area of the surface generated by revolving the curve about the x axis y=√x, 0≤x≤2( Note: I…

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Q: 3. 3) 6) X= y 〇s454 6) Find the area 0f the surface of rotation Created by ocyEd curve about the 3.…

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

Q: 1) Find the area a) Inside the cardioid r= 2 cos (0/3) and outside the circle of radius r = v2…

A: q-1(a) find the area inside the cardioid r=2cosθ3 and outside the circle of radius r=2 centered at…

Q: 2. Find the length of the curve over the given region. (a) r = e", 0 € [0, 2], (b) r = 8+ 8 cos 0, 0…

A: If we have a curve r=fθ then the length of the curve for θ∈a,b is L=∫abfθ2+dfθdθ2dθ Part(a) We have…

Q: Question 10 Find the area enclosed by the curves y = 2x √3- π ® ²-√√4-. (A) А Im 21/12-4/09/20 7x D…

A: The equation of curves are: C1: y = 11-9x2C2: y = 2 To evaluate: The area enclosed by the curves.

Q: 5) Determine the area of the surface obtained by rotating the arc y = Vx –1 around the x- axis from…

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Q: 7. The integral used to find the length of the curve y=xbetween x = 0 and x = 4 is (Circle your…

A: I have Provided this answer in step-2.

Q: 10. Consider the region R shown in the following figure, which involves the curves of equations: ex…

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Q: 1) Find the area of the region bounded by the curves: x=2y2 and x=16+y2 2) Find the area of the…

A: Important points: 1. First we will draw both the parabolas by finding their vertex. 2. Then we will…

Q: 4/ Find the area of the region enclosed between the curves y= cos 2x y=0, x=TT/4, x= TT/2 ? ans/ 1/2

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 1. Find the surface area generated by rotating the curve y = /2x + 4 about the x-axis for x = 2 to x…

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Q: 1. Find the surface area of the solid obtained by revolving the curve y = √25-x from = 9 to x = 16…

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Q: 1.2. The area of the region bounded by the curves sin r, y = cos r, I= 0 and a equal to A. 1.4142…

A: Given curves are y=sinx, y=cosx ,x=0 and x=π/4

Q: The area between the two curves in * the figure below is y = cos x y = sin 2x T/6 T/2

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Q: (b) Find the area under the curve defined parametrically as x=t²-1 and y=t³-t for 0≤t≤1

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Q: Find and shade the area to the left of cach positive z value. Given Curve 1. C-0.9s 2. z= 1.47

A: As per company guidelines I solved exactly three subparts of the question.thank you

Q: x3 1 +-from x = 1 to x = 2 is 12 Question #1- Find the surface area generated when y=+– from x = 1…

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Q: 1(a) Find the arc length of the curve 2x = 3y2/3 over the interval from y=0 to y=1  1(b) Find the…

A: (a) The arc length of the curve 2x=3y23 over the interval y=0 to y=1 can be calculated by using…

Q: Question 8 Calculate the area of the surface generated when the curve, y = Vx is revolved on the…

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Q: %3D Question 3: Find the area between the curve y = 4 – x2 and the line y = -x + 2.

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Q: Find the area of the surface generated by revolving the given curve about the y-axis. 8zy = 2y + 1,…

A: A curve is given by, 8xy2=2y6+1 where 1≤y≤2. The objective is to find the area of the surface…

Q: Question 3 Find the area enclosed by the curves y y = 2 V1- 9x2 O V5- 9. 2n B 3 5n D 6

A: Solution is given below:

Q: Q#4 a. Find the area of the surface generated by revolving about the x - axis the portion of the…

A: Given that: x23+y23=1 To solve: x23+y23=1y23=1-x23y=1-x2332…

Q: 2. Find the area of the region that lies inside both curves * r = 4 sin(0) and = 4 cos(0) 2л — 1 ●…

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Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y=x²-In(x),…

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Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y =x² - In(x),…

A: The derivative of a function gives the rate of change of it with respect to some other variable.…

Q: Question 46 Find the volume of the solid that results when the region in the first quadrant bounded…

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Q: Question 7 Calculate the area of the surface generated when the curve, f(x) = x³/2 . x1/2 on [1,2 ]…

A: Here f(x)= x32-x123 on the interval [1,2]it is revolving about the x-axis .The surface…

Q: 1 (#3) Find the surface area for y = 3 on [0, 3] rotating on the x- axis.

A: Given an equation of a curve, The solid will form by rotating the curve about the x-axis.

Q: the surface area of a .17 rotating the curve y = x power 3 around the x - axis between the points…

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Q: 25) Find the areas of the regions eoclosed by the lines and curves y 2 sin x and v sin 2x, 0SIST

A: To find the area enclosed by the given curves: y=2 sin x and y=sin 2x, 0≤x≤π The area enclosed by…

Q: Find the surface area of the region that comes from rotating the given curve about the x-axis: x = 4…

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Q: for the Surface Area below .. what is * ?the radius of revolution Q3/ The arc of the curve x=Vy,…

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Q: Find the area of the surface generated by -y + e revolving the curve x = 2 Osys In 7 about the…

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Q: 4. Find the area of the surface formed by revolving the graph of f(x) = x² on the interval [0,…

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Q: Question (4): Find the area of the region bounded by the curves: y = cos(nx) and y = -1+ 4x?

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Q: 2. y = ln(x²-1), 2 ≤ x ≤ 3 ;y-axis

A: The given problem is to find the area of surface of the revolution of the given curve over the given…

Q: 17. Find the area of the region that lies inside the first curve and outside the second curve. r = 2…

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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.