Surface Area 7. At points on the curve y = 2Vx, line segments of length h = y are drawn perpendicular to the xy-plane. (See accompanying fig- ure.) Find the area of the surface formed by these perpendiculars from (0, 0) to (3, 2V3). 2V3 (3, 2/3) y = 2Vx 0. 3

Q: Q. 3 The solid of revolution obtained by rotating the region under the curve y = f(x), a sx sb,…

A: Formula: uv'=uv'+vu' Formula: sin x'= cos x The given function is: f(x)=x sin x, 1≤x≤2 The surface…

Q: 1-12 Find the volume of the solid obtained by rotating the region bounded by the given curves about…

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Q: 1. Find centroid of the solid in the first quadrant, bounded by the x-axis, and curves y = x², x of…

A: Given: To calculate the centroid that is bounded by the x-axis and the curves are y = x2, = 2y - y2.…

Q: Find the area of the surface given by z = f(x,y) over the region R.   R:  The triangle with…

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Q: 17-18 ▪ Use a CAS to find the exact area of the surface obtained by rotating the curve about the…

A: CAS is Length of arc that is using length of arc formula to evaluate the integral Also given area of…

Q: 5- Finding the areas of the surfaces generated by revolving the curves in exercises about the…

A: 1. Given that, the equation is y=2x-x2 and 0.5,1.5, the solid generated about x-axis. Note that. the…

Q: 1. Find the volume of the solid obtained by rotating the region bounded by the given curves about…

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Q: 3.Obtain the centroid of the solid formed of the area bounded in the first quadrant by y = 2x7, the…

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Q: 12. The part of the cylinder x² + z² = 16 that lies between the planes x Find the area of the…

A: We know that if height of a cylinder be h Units and radius be r units then curved surface area of…

Q: The region bounded by the parabola y=x2 +1 and the line y = x + 3 is revolved about x axis. The…

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Q: 19-22 Use Simpson's Rule with n- 10 to approximate the ared of the surface obtained by rotating the…

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Q: 2. The x-coordinate of the centriod of the area of the region defined by 0zy2x(x-1) 18 A. 1 B. C.2 D…

A: To Determine :-  The region bounded by y = x2 + 4 the lines y = 8 and x =0 is rotated .

Q: 0:32:4 Consider the solid obtained by rotating the region bounded by the given curves about the…

A: Given problem:- Consider the solid obtained by rotating the region bounded by the given curves about…

Q: ind the volume of the resulting solid if the region under the curve  y = 8/(x2 + 3x + 2)  from x =…

A: Consider the curves y = 8x2+3x+2, x=0, x=1 about x-axis For this region of the disk is y = 8x2+3x+2…

Q: a. Set up an integral for the area of the surface generated by revolving the curve x b. Graph the…

A: Consider the given: x12+y12=6Limits25,1to1,25x+y=6x=6-yx=6-y2dxdy=y-6y

Q: 15. Find the surface area generated by revolving about the y-axis that part of the curve y = In x…

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Q: Find the area of the surface generated revolving the given curve about the y-axis. 1. X=y^3 , 0 is…

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Q: Find the area of the surface generated when the given curve is revolved about the given axis. 5 9…

A: Use formula of area of surface generated about y axis

Q: '= xi through the surface S oriented downward and parameterized for 0 < 8 < 4,0 < t<n/6 by * = e°, y…

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Q: 39.The region enclosed by the curve y= x+- and the lines y= % x, x= 1 and x = 2 is rotated %3D %3!…

A: Note: Since you have posted multiple questions we will solve the first question for you. To get the…

Q: I the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A: To Find:  Volume V of the solid obtained by rotating the region bounded by the given curves about  y…

Q: 10. Find the volume of the solid of revolution formed by rotating the region enclosed by the curves…

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Q: (c) Sketch and shade the region between the curves y=x' and y - x, xe(1, 2]. i Calculate the area of…

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Q: 1. Find the area bounded by the curves y = x², y=A and x=B. 2. Find the volume of the solid…

A: Firstly, find the area bounded by the curve y=x2, y=16 and x=5. That is the area between the upward…

Q: |Consider the surface z = x' + 2y? – 4ry. 1. (a) Graph the surface using technology. Make a rough…

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Q: 3. Let R be the region below bounded by the parabola y = 4 - 2² and the lines 3x - 2y +3=0 and y =…

A: The region R is bounded by the parabola y=4-x2 and the line 3x-2y+3=0 and y=0.

Q: 1 (x² +2)% 3 4. Consider the curve y = 0<x<1 a) Find the length of this curve b) Find the volume of…

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Q: The area under the curve 4y2 = (x? + 1)3 was rotated about a line located to the left of y - axis by…

A: The area under the curve 4y2=169x2+13 is rotated about a line located to the left of y-axis by three…

Q: 1-12 Find the volume of the solid obtained by rotating the region bounded by the given curves about…

A: Let's find.

Q: 1-12 Find the volume of the solid obtained by rotating the region bounded by the given curves about…

A: Recall:     Suppose that x=f(y) is a continuous non-negative function on the interval c,d.The volume…

Q: b) [ bounded 1: Find the volume of the solid obtained by rotating the region by the curve about the…

A: Graph:

Q: 9 (2). Consider the region R shown in the following figure, which involves the curves of equations…

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Q: Find the area bounded by the parabolas y2=4x and y2

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Q: 4. Consider the curve y=- + 2)" 0<x<1 a) Find the length of this curve b) Find the volume of the…

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Q: Given a surface z = 9 - x² - y². (a) Find the volume of the solid lying under the surface and above…

A: Note : The volume V of the solid lying under the surface z=f(x,y) and above a bounded region R in…

Q: Find the area of the surface generated revolving the given curve about the x-axis. 1. Y=3√y , 1 is…

A: 1.we have given  x=3y 1 is less than equals to y is less than equals to 8  surface…

Q: could i please get help with 9c?

A: Graph the given functions using graphing calculator. Shade the bounded region. It will rotate about…

Q: 1. Find the volume of the solid created by rotating the region enclosed by the curve x² + 4y2 = 4 ,…

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Q: For question 8 rotating the 8. use the method of cylinders to determine the volume of the solid…

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Q: As viewed from above, a swimming pool has the shape of the ellipse y2 1, 400 x2 2500 where x and y…

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Q: 3) A curve C is the boundary of a shaded region D which defined by y = 2x² - 4 and y = 2x in…

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Q: 10. Find the volume of the solid generated by revolving the area enclosed by the loop of the curve…

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Q: 5æ? about the y axis for 3 < x < 8 Find the area of the surface obtained by rotating the curve y No…

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Q: Using Green's theorem in the plane, evaluate $ (ry² dy - x²y* dx). where C is the triangle with…

A: Using Green's theorem in the plane, we have to evaluate ∮Cx3y2dy-x2y3dx, where C is the triangle…

Q: 15. Find the surface area generated by revolving about the y-axis that part of the curve y = In x…

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Q: V6 sin z, and the lines Problem : Find the volume of the solid of revolution bounded by the curvey…

A: first we need to plot the graph and the limits given, to know how the figure looks like

Q: Sketch and shade the region bounded by the curve y = x² - 4 for xe [0, 2]. i. Calculate the area of…

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Q: {(x, y) | 1 ≤ (x − 3)2 + (y − 4)2 ≤ 49} Sketch and shade the region in the xy-plane

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Q: 9:(a): Find the area bounded by the curve y = = -x, the line y = x, and the line y= 2. (b) : Find…

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Q: 2. Find the absolute extrema of the given surface on the indicated region. Surface : x? + y² – 3z =…

A: The solution are next step