Use the cylindrical coordinates to evaluate the triple integral

Q: FIND THE CENTROID OF THE AREA BOUNDED BY THE CURVE r = a (1 + sin 0).

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Q: Find the lateral surface area of the cone generated by revolving the line segment y = x/2, 0 ≤ x ≤…

A: Given equation of line segment is  y = x/2, 0 ≤ x ≤ 4,

Q: Use the triple integral in spherical coordinates to evaluate where G is bounded by yz-plane , x = /9…

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Q: Set up a triple integral in spherical coordinates to c

A: Given, the solid bounded above by the cone x2+y2=z2and bounded below by the sphere…

Q: Find the surface area for x=3( θ – sin θ ) , y= 3(1-cos θ ). , when rotated along the x axis.

A: Given x=3θ-sin θ,  y=31-cos θ  The surface area is rotated along the x-axis. Then y=0, 31-cos…

Q: Find the area of the surface generated by revolving the curve y = 2Va, 0 <x < 3, about the x-axis.

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Q: Parametrize the osculating circle to y = √x at x = 4.

A: Given that the osculating circle  y = x

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: Convert dzdydx /9-x-y Into an integral of cylindrical coordinates

A: Given∫03∫09-x2∫3--x2-y2x2+y2 dz dy dxTo convert it into polar coordinateswe know thatx=rcosθ,y=rsinθ…

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

A: given,         a sphere of radius R

Q: Find the lateral surface of the cone generated by revolving the line y = mx from x = 0 to x = 1…

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Q: Convert the integral 9-x²-y? Vr2 + y² + z² dzdydx to spherical coordinates then evaluate.

A: Consider the triple integral         I=∫03∫09-x2∫09-x2-y2x2+y2+z2 dz dy dx in cartesian coordinates.…

Q: ローペープ 8-x²-y z?dzdxdy. Use cylindrical or spherical coordinates to evaluate the integral.

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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: !! Evaluate the triple integral 2.rz dz dy dx by changing in to cylindrical coordinates. 0 0

A: Transformation from Cartesian (x, y, z) to Cylindrical coordinates:

Q: Find the moment of inertia of the solid formed by revolving about ox the area bounded by a^2y=x^3,…

A: The given problem is to find the moment of inertia of the solid formed by revolving about an x-axis…

Q: change the iterated integrals to cylindrical coordinates 9-z²-y z ydzdydr -3 9-z2

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Q: Use double integral polar coordinates to find the area of the portion of the surface 3z = xy that…

A: Area of the surface given by the equation z=fx,y is given by S=∫∫A 1+zx2+zy2 dA where A is the…

Q: choose The correct ansuer when transforming The triple integral 3. メーム 9-xーy 9-x2 to spherical…

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Q: 2. Use integration in cylindrical coordinates in order to compute the vol- ume of:

A: Given,       U=x, y, z: 0≤x2+y2≤1, 0≤z≤5-x-y

Q: Evaluate the spherical coordinate integral.

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Q: V4-y² 4-x²-y² LL" L +yi + z°dzdsdy -2 Jo /4-x²-y²

A: Consider the given information: ∫-22∫04-y2∫-4-x2-y24-x2-y2y2x2+y2+z2dzdxdy To calculate integral by…

Q: 2. By changing to cylindrical coordinate, evaluate So 1-x²1542x² dzdydx

A: Introduction: Sometimes, a triple integral given in the rectangular coordinate system is very…

Q: Express the given rectangular triple integral as a triple integral in cylindrical coordinates.…

A: Express the given rectangular triple integral asa triple integral in cylindrical coordinates…

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: Solve the area of the surface of the revolution generated by revolving the arc of the curve, x= y³…

A: A detailed solution is given below.

Q: Evaluate the surface integral

A: Given,                ∫∫S8z2dS Where S is the boundary of the cube C=-1, 1×-1, 1×-1, 1.

Q: Caluelate the integral using polar coordinates dA ,

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Q: Use spherical coordinates to evaluate the integral •√₁-x² √√₁-x²-x² (x² + y² + ²)dzdydx.

A: To evaluate the integral using spherical co-ordinate system :-

Q: Find the surface area of the solid gained by revolving the curve 0 < x < 14, about the x – axis. 14'

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Q: Find the moment of inertia about a diameter of a thin spherical shell of radius a and constant…

A: Let the diameter lie on the z-axis and let f(x,y,z) = x2+y2+z2=a2; z≥o  be the upper hemisphere…

Q: 1-z z dz dy dr V1-z 3x2+3y2

A: Triple integral is used to integrate functions of three variables over a three-dimensional region.…

Q: Convert the integral from rectangular coordinates to both cylindrical and spherical coordinates |–x²…

A: Given triple integral, ∫01∫01-x2∫01-x2-y2zx2+y2dzdydx To convert this integral from rectangular…

Q: .Estimate vu in cylindrical form, in the orthogonal curvilinear coordinates

A: Given: We consider elliptic in cylindrical form .

Q: Use cylindrical coordinates to evaluate the integral 2 /2x-x x²+y? 2 2 s Vx´ + y´ dzdydx 2 -V2x-x

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Q: Find the area of the surface generated by revolving the curve y=- 24 .Osxs/6. about the x-axis.

A: area = ∫06 ydx area = ∫06  x3dx/24 area = [x4/96]60 area = 6*6/96 - 0 area = 3/8

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: Find the centroid by revolving the given plane area about the indicated axis y^2=5-x, x=0 ; about…

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Q: Find the moment of inertia of a right circular cone of base radius a and height h about its axis.…

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Q: Evaluate the integral **** + y dzdyd by changing to cylindrical coordinates

A: To evaluate the integral using cylindrical coordinate  ∫-33∫09-x2∫09-x2-y2x2+y2dzdydx

Q: Evaluate the surface integral.

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

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Q: Find the area of the surface generated by revolving the curve 1 V1+e*, 5x 0 < x < 2 around the…

A: We can find the area of the the surface as follows

Q: Find the surface area obtained by rotating y = V9 – x² -2sxs-1

A: As we know that; The expression for the area of surface rotating about the x-axis. S=2π∫abfxf'x2+1dx…

Q: Find the area of the surface generated by revolving the curve y = 3/x, 1 < x <4 about the x axis.

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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…

Q: Convert to cylindrical coordinates and evaluate the integral 5 /25–x² 6 !!! dzdydx x² + y- 0 0 0

A: Conversion of cartesian co-ordinates into cylindrical co-ordinates. φ is angle made by vector with…