Find the surface area of the portion of the sphere of radius 4 that lies inside the Fylinder x2+y? = 12 and a bove the xy-plane. where: X= Peos e sing » y = P sine sing Z = Pcos Ø

Q: Find the area of the surface generated by revolving x= 4/9 - y,0sys about the y-axis. 16 x=49-v 12

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Q: Use Simpson's Rule with n = 10 to approximate the area of the surface obtained by rotating the curve…

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Q: Calculate the area of the surface generated when the curve, y = Vx is revolved on the interval [1<…

A: y=x3then x=y3 area of the surface=∫12xddy=∫12y3dy=y4412

Q: Find the volumMe generated by revolving the area bounded by the giveN Curve and avd lines y = x', x…

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Q: 2. Find the surface area generated by revolving the circle x = cost, y = 1 + sint, 0sts2n over x -…

A: Use formula of area about x axis

Q: Find the surface area generated by rotating y=sin x. 0 ≤ x≤ π about the x-aixs.

A: Area of surface problem....

Q: Find the area of R. Set up a (sum of) definite integral(s) that is equal to the arc length of the…

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Q: The surface area of the surface generated by revolving y =x³ , 0 Sx<1 about the x- axis is

A: Given : y= x3    ,  limit  0 to 1

Q: Find the area of the surface generated by revolving the curve x = Vy, 0<y <4, about the y-axis.

A: We will use standard method.

Q: Find the surface area of revolution about the x- axis of y = 3 sin(5x) over the interval Preview

A: Given curve is y=3in(5x), firstly, we will find dy/dx

Q: Find the area of surface revolution, when x=1+cosθ. , y=sinθ Where 0≤θ≤2π

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Q: Find the area of the surface generated by revolving the C = ((x, y): x = 3 (t – sin t), y = 3 (1-…

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Q: (3) Use line integral to find the area af the surface thet extends upward from the Part of the…

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Q: Find the volume of the solid generated by revolving the area bounded by the given curves about the…

A: • This is a problem based on the applications of definite integral.  First we have to identify the…

Q: Find the lateral surface area of the cone generated by revolving the line segment y = x/6, 0 sx s2…

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Q: Determine the moment of inertia of the area bound by the two curves about the x and y axis. y y = x?…

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Q: Find the area of the surface generated by revolving the curve 6a² xy = y + 3a from y= a to y = 3a…

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Q: Find the surface area of revolution generated by revolving the curve y= (3x)5 over about the y…

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Q: The density of a spherical solid of radius 2, centered at the origin, is given by D(ρ) = 4ρ grams…

A: Consider the following figure.We have find the volume of the solid above the plane z = 3.

Q: aluate the integral flR (1– -) dA where Ris the circle of radius 2 centered at the origin on the…

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Q: Reduce the surface integral ( S A.ds) of a cube of sides parallel to the three perpendicular axes,…

A: Here we can use divergence theorem to reduce the given surface integral. Divergence theorem states…

Q: Find the area of the surface generated by revolving the curve x = a cos θ,       y = b sin θ, 0 ≤ θ…

A: The curves x=acosθ,y=asinθ, and 0≤θ≤2π, we have to find the area of the surface generated by…

Q: Find the area of the surface generated by revolving the region bounded by, 1 1syss 16y4 y6 1<y< 5 6.…

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Q: Use Simpson's Rule with n = 10 to approximate the area of the surface obtained by rotating the curve…

A: Given that, the function is y=secx and the interval is 0,π3. Note that, the formula for the surface…

Q: Set up an integral for the area of the surface generated by revolving the curve y=x about the…

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Q: Find the area of the surface generated by revolving y = Vx +1 from r = 1 to x = 5

A: The objective is to find the area of the surface generated by revolving y=x+1 from x=1 to x=5.

Q: Find the volume of the region bounded above by the sphere r = 2a cos0, and below by the cone = a…

A: Given: the sphere r=2a cos theta , cone ϕ=α0&lt;α&lt;π2

Q: y = } + sxs1 <x<1 2

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Q: Find the surface area generated by revolving y=7x+6 about the x axis on the interval [0,6]

A: We need to find the surface area generated by revolving y=7x+6 about the x axis on the interval…

Q: Q3: Develop the lateral surface of a hexagonal prism of base edge 20mm a on its base on HP such that…

A: Given: To explain the given statement as follows, To develop the lateral surface of a hexagonal…

Q: Find the surface area generated by revolving Y=(x^3)/6 about the x axis over the interval [0, sqrt6]

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Q: Find the area of the surface generated by revolving the given curve about the indicated axis. 1. x =…

A: Consider two parametric equations and with . Then the area of the surface obtained by rotating…

Q: Find the area of the surface generated by revolving about x-axis the part of the curve y = sin x,…

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Q: Find the area of the surface generated by revolving x = 6t and y = 4ť (0 < t < 1) X

A: answer is in next step

Q: Find the moment of inertia for a quarter of a regular circular plate of radius (b)Find Mom ent of…

A: Given: (a) A quarter of a regular circular plate of radius (b) The parabola Y=x2b and the line y=b

Q: Find the area of the surface generated by revolving the given curve about the yy-axis.…

A: Given curve is, x=25-y, -1≤y≤0 Now, differentiating with respect to y we get,…

Q: Find the moment of inertia of the area bounded by a parabola y?=4(29)x , Osys29, its axis with…

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Q: Find the area of the surface obtained by rotating the curve. y=x+, 1<x< 2 rotated about the x-axis…

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Q: Use a line integral to find the area of the surface that extends upward from the parabola y = x² (0…

A: We have to use a line integral to find the area of the surface that extends upward from the parabola…

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

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Q: Compute the line integral Sy?a dl where y is the part of the circle centered at the origin and of…

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Q: Use spherical coordinates to calculate the integral SSgr+y°dV over the region E which is the portion…

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Q: HW: Find the area of the surface generaled by revolving 1. LIIC 2. y = Vx- xã , 1 sxs3 about x2, 1…

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Q: 2. Determine the area of the surface generated by revolving a given curve about a given axis. a.…

A: Formula to find the surface area by revolution helps to find the required surface area. Formula to…

Q: Find the area of the surface obtained by rotating the curve y = x² - In(x) about the y-axis for 3…

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Q: Use a line integral to find the area of the surface that extends upward from the parabola y =x…

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Q: Find the moment of inertia about the x-axis of a thin plate with density 8=1 bounded by the circle…

A: Given: The density of the plate =1 The plate is bounded by the circle =x2+y2=16

Q: (b) Find the volume of the solid generated by revolving the region enclosed by the curve y = 6x – x…

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Q: Find the area of the surface generated by revolving the curve x = Osys2, about the y-axis

A: Given: The curve is x=y32, 0≤y≤2 about the y-axis The formula for find the area of the surface is…