Use double integral in polar coordinates to find the area of the portion of the sphere

Q: 10 Find the area of the surface generated by revolving the region bounded by. ISKSS about the…

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Q: Use polar coordinates to evaluate the double integral int int _R (4+x) dA , where R is the region…

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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: Use a double integral in polar coordinates to find the region described: The region inside the…

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Q: Sketch the region enclosed by the curves and find its area. 1 х — 0, у — 1, у — е NOTE: Enter the…

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Q: Polar Integrals! Please show all work neatly! Thanks

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Q: Use a double integral in polar coordinates to find the volume of the solid in the first octant…

A: Given the region is bounded by the ellipsoid 9x2+9y2+4z2=36 and the planes x=3y, x=0, z=0.   Double…

Q: Please provide me with a worked example of finding the area bounded by a simple polar curve. Thank…

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Q: Find the area of the triangle with vertices (0,0), (2, 0) and (2,2) by computing a double integral…

A: As per the question we are given a (right-angled) triangle with vertices at (0,0), (2,0), (2,2) And…

Q: . Use a triple integral to derive the formula for the volume of the ellipsoid *+ + = 1.

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Q: Use a triple integral in spherical coordinates to derive the volume of a sphere with radius a.

A: To find - Use a triple integral in spherical coordinates to derive the volume of a sphere with…

Q: . Sketch the region of integration and change the integral to polar coordinates. V4-x* * * dydx

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Q: Draw the 2D and 3D pictures associated with each integral. Indicate the axis of revolution, show a…

A: Let fx=sinx, 0≤x≤π. It's figure is below

Q: Use spherical coordinates to compute the surface area of a sphereof radius R.

A: given,         a sphere of radius R

Q: Use a double integral in polar coordinates to find the volume of the solid bounded by the graphs of…

A: Use a double integral in polar coordinates to find the volume of the solid bounded by the graphs of…

Q: Find the centroid of the area bounded by the given curve r = 3sin θ in the first quadrant.

A: Double integral is used to integrate the function of two variable over two dimensional region.…

Q: Use a triple integral to find the volume of the solid shown in the figur z = 16 – x² - y²

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Q: Sketch the region and use a double integral to find its area. The region bounded by the cardioid r=…

A: The cardioid is r=-31-sinθ, θ r=-31-sinθ 0 r=-3 π6 r=-32 π4 r=-31-12 π3 r=-31-32 π2 r=0…

Q: Evaluate the integral xyzdV where E lies between the spheres with radius 2 and 4 and above the cone…

A: Using spherical coordinates,

Q: Use triple integral to show that the volume of a sphere with radius 'a' ra". is

A: We have to use triple integral to show that volume of sphere with radius ' a ' is 43π a3. Equation…

Q: Find an integral for the area of the surface obtained by rotating y = √25-x, 9 ≤x≤ 16, about the…

A: To find an integral for the area of the surface obtained by rotating the below equation about the…

Q: Write a triple integral in cartesian or spherical coordinates for the solid and solve for the volume

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Q: Sketch the region enclosed by y=2x and y=6x^2 Use an integral to calculate the area of this…

A: Given : y = 2x y = 6x2    NOTE :- If two functions f(x) and g(x)g are plotted on a plane, for the…

Q: ху 3D 9, у %3D х, у %3D 0, х %3D 9

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Q: In spherical coordinate instead of one in rectangular coordinates, when is it advantageous to use a…

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Q: Sketch the region enclosed by the curves y = (x-2)2 and y=x then find its area using the…

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Q: Use a double integral in polar coordinates to find the area of the region. The region inside the…

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Q: iii) Set up an integral for the area of the surface generated by rotating the curve about the…

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Q: Write an integral for the area of the surface generated by revolvingthe curve y = cos x, -π/2 ≤ x…

A: Given data: The equation of a curve is: y=cosx. The limit of x is: .   The expression for the…

Q: Sketch the region of integration for the following integral, then, change the integral from the…

A: Explanation of the solution is given below...

Q: caleulate the Hriple integral with spherical coordinates

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Q: Sketch the region and use a double integral to find its area. The region bounded by the cardioid r=…

A: We have to find the area of the region bounded by the cardioid r=-51-cosθ. Using a graphing utility,…

Q: Sketch the region enclosed by the curves x = sin 7y and x = 14 y, and compute its area as an…

A: Recall: Area between the curves :Given that x=f(y) and x=g(y) and f(y)≥g(y) on c,d, then the are…

Q: Find the Integral of Area of a Surface of Revolution

A: Given x=etcosty=etsint0<t<π2

Q: Describe in words when it is advantageous to evaluate a triple integral in spherical coordinates and…

A: Given:-               Describe in words when it is advantageous to evaluate a triple integral in…

Q: Use a double integral in polar coordinates to find the area of the region bounded on the inside by…

A: The given graphs are a circle with radius = 4, and a cardioid r = 4(1+cos θ). On plotting, we obtain…

Q: Determine the area of the region R that lies (between the parabolic curve and the straight line)…

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Q: Use a double integral in polar coordinates to find the area of the region bounded on the inside by…

A: Solution:-

Q: Find the volume enclosed by the torusp = 4 sin().-

A: The volume is given by: V=∫∫∫dv In spherical co-ordinate dV=ρ2sin φ dρ dφ dθ

Q: + 1 -оу-х -oy=x2

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Q: Use spherical coordinates to find the volume of a sphere of radius 2 from which a central cy tinder…

A: Let us assume that , x2+y2+z2=22x2+y2=1 The graph will be :

Q: Sketch the region enclosed by the curves 4x+y2=12 and y=x then find its area using the appropriate…

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Q: : Find the area of the region bounded by x = -2, y = 0 and y = v9 – x² in the second quadrant by…

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Q: Convert the integral into spherical coordinates. Int[-3,3]  Int[0,sqrt(9-x^2)]…

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Q: Use a double integral in polar coordinates to find the volume of a circular cylinder of radius 13…

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Q: 36-х? —у? y'dzdydx by re-writing the integral in spherical coordinates. Evaluate 3x²+3y²

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Q: Write a double integral that represents the surface area of the portion of the plane z = 3 that lies…

A: Given: A double integral that represents the surface area of the portion of the plane z = 3 that…