52. Show that a spherical cap of height h and radius R (Figure 19) has surface area 2n Rh. Rogawski et al., Calculus: Early Transcendentals, 4e, © 2015 Company an and 8.2 EXERCISES FIGURE 19

Q: 4. Find the volume of the wedge cut from the first octant by the cylinder z = 12 – 3y², and the…

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Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r = 80,0 < 0 <…

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Q: 50.) Show how to use a line integral to find the area of a circular disk of radius r

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Q: 5- 4- Find the volume of the solid created by rotating the following curve y = 3vx about the y-axis.…

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Q: Compute the area of surface generated by revolving the four-cusped of hypocycloid x⅔+ y⅔ =a⅔ about…

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Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r = 30,0 < 0 <…

A: Given, r=3θ,  0≤θ≤5.4

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. Show that an equilateral triangle can be inscribed in the epitrochoid and that its centroid is on…

A: An equilateral triangle can be inscribed in the epitrochoid and that its centroid is onthe circle of…

Q: Find the area of the surface generated by revolving the curve about the y-axis. y=4-x², 0≤x≤2.

A: In this question we have to find the area of the surface generated by revolving the curve about the…

Q: Evaluate ff. xyz ds, over that part of a sphere of two units radius and centre at the origin Which…

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Q: Find the area of ​​the rotating surface that occurs by turning circle x2+y2=4 around line x=2 .

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Q: Consider a thin plate of constant density d lying in the regionbounded by the graphs of y = √x and x…

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Q: 4. Illustrate and find the center of mass and moment of inertia with respect to x and y for the…

A: y = f(x) =4-x2   only in First quadrant…

Q: how by integration that the centroid of a uniform semi-circular lamina of radius a from ne centre is…

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Q: 5 Find the lateral (side) surface area of the cone generated by revolving the line segment y = x,…

A: If the curve y = f(x) , a≤x≤b is rotated about x-axis, then the lateral surface area is given by…

Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r = 30, 0 < 0…

A: According to the given information, it is required to find the area enclosed by the given curve.

Q: ve = Vti + Vrj + (2t – 1)k is tangent to the surface x+y-z = 1 Show that the curv when t=l

A: Consider the given curve r=ti+tj+2t-1k And the given surface x2+y2-z=1 First, write the curve in…

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: What is the surface area generated by revolving the parabola y = x squred from x = 0 to x = square…

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Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r=2θ, 0≤θ≤4.5…

A: Given that  r=2θ, 0≤θ≤4.5 To Find the area enclosed by the closed curve obtained by joiningthe ends…

Q: A thin plate part with a mass density equal to 1 and shape as shown in Figure 2 has an edge curve C…

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Q: Determine the area of the surface generated by revolving y=x³ on (0,1), about the x-axis.

A: The given curve is y=x3  on 0, 1 about x-axis. This implies that,…

Q: Find the area of the surface generated by revolving the curve about the indicated axis. SET UP ONLY…

A: The area of the surface generated by revolving the curve around the y axis can be given as:…

Q: Find the center of mass of solid revolution if an area in Ist Quadrant (Kuadran Pertama) bounded by…

A: Given functions are Intersection points Area of region is Centre of mass revolution

Q: Evaluate the integral hipxp hx^ 7 and the hyperbola ry = 13. where R is the region bounded by the…

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Q: Find the surface area obtained by revolving the parabolic arc y2=x from (0, 0) to (9, 3) about the…

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Q: Find the Area of the Surface obtained by rotating the curve about the x-axis y = cosh x, 0≤x≤1

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Q: 3. Find the surface area generated by rotating y=- bounded by y=0_ x=0 , and x=9 about the the…

A: Surface area generated by rotating a curve y = f(x) about the x-axis from x = a to x = b is given by…

Q: (1 point) Calculate the volume under the elliptic paraboloid z = 2x2 +3y2 and over the rectangle R =…

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Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r = 40,0 ≤ 0 ≤…

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Q: Find the area of the surface obtained by revolving the graph of x = y³ on the interval [0,1] about…

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Q: Calculate the volume under the elliptic paraboloid z = 4x² + 6y2 and over the rectangle R = [-2, 2]…

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Q: Find the area enclosed by the closed curve obtained by joining the ends of the spiral r = 10, 0 < 0…

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Q: Calculate the volume under the elliptic paraboloid z = 4x2 + 6y2 and over the rectangle R = [-2, 2]…

A: The solution for the above question is shown below.

Q: Find a center of mass of a thin plate of density 8 = 5 bounded by the lines y = x and x=0 and the…

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Q: 7 Find the area of the surface generated by revolving x = 2/4-y, 0sys about the y-axis.

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Q: 9. Find the demensions of the right circular cylinder of largest volume that can be inscribed in a…

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Q: Find the center of mass of a thin plate of constant density & covering the given Region enclosed by…

A: Curve 1: y=x-x2 Curve 2: y=-x We have to find the center of mass.

Q: Evaluate the line integral a xds where C is one quarter of a circle (in the first quadrant) of…

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Q: Determine the area of the surface of revolution of x=sqrt{y} from (1,1) to (2,4), rotated about the…

A: The equation is x=y.   Determine the derivative dxdy=12y   The formula for the area of surface…

Q: Find the area of the surface generated by revolving the curve y = 2√x, 1≤x≤2, about the x-axis.

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Q: Assume we wish to to make a right cylindrical can with a bottom and no top, and with a capacity of…

A: Solve it

Q: The arc y=2 sqrt(x) from x∈[4,16] is rotated about the x axis. Find the exact surface area…

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Q: (a) Find that the area of the plane region lying to the right of the parabola x = and to the left of…

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Q: D Find the area of the surface generated by revolving the region bounded by, 1 1 <x < 5 4 8x2 about…

A: In the question we have to find area of the given function.

Q: The center of mass of a lamina of total mass 5 has coordinates (2, 1). What are the lamina’s x- and…

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Q: Determine the area bounded by the conic sections y = x² – 6² and y = 6² – 2². O 576 O 183 O 281 O…

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Q: Find parametrization of the horizontal circle of radius 4 with center (5, -2, 6). r(t) = %3D

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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…