. Parametrize a cone lying over the x, y plane with its tip at the point (3, 4), height 3, and its maximum radius 6.

Q: For F(x,y,z) = (6y-4xz/(z2+1)2)i + (-2yz-6x/(z2+1)2)j + (-3/z2+1)k,  Calculate the net flux through…

A: consider the equation

Q: Find the area and centroid bounded by the curve 5y? = 16x and the curve y2 = 8x – 24.

A: Since you have asked multiple question, we will solve the one question for you. If you want any…

Q: 2. Let D = 2xyā, + 2(x² + z²)d, + 4yzd, C/m² and evaluate surface integrals to find total charge…

A: given D→=2xy ax→+2x2+z2 ay→+4yz az→ it is known that ρ=∇·D→ it is known that…

Q: Let E be the solid bounded inside the ellipsoid = 1, where a, b and c are positive numbers. Evaluate…

A: E is the solid bounded inside the ellipsoid x2a2+y2b2+z2c2=1Where a, b, and c are positive…

Q: (5) Use Stokes' Theorem to find the line integral |(* + 2y°)i + (y + z°) +(= + 2r*)k) • dř where C…

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Q: Use cylindrical coordinates to evaluate the integral 2²dV where E is the solid that lies within the…

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Q: According to the divergence theorem, one of the following integrals represents the surface integral…

A:

Q: For an area A in the x-y plane, in the expression I₂ = Ix+ly, the term /₂ is the: Minimum…

A: Introduction : As per definition, The polar amount of inertia is the total sum of the moment of…

Q: 4. Find the volume V of the solid S that is bounded by the elliptic paraboloid defined by 2x2 + y2…

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Q: 7. Use Stokes's Theorem to write S.(2y² + 6x*)dx + (2x² + 7y³)dy+ (2z° – yz)dz as a surface integral…

A:

Q: compute the line integral f(x, y) ds for the given function and path or curve. f(x, y) = x – y, the…

A: Given: fx,y=x-y To Find: Line integral ∫Cfx,yds over the unit semi-circle x2+y2=1, y≥0

Q: Use Stokes' theorem to evaluate line integral| (z dx + x dy + y dz), where C is a triangle with…

A:

Q: Evaluate the surface integral I F. dS when F(x, y, 2) = y²i+ 3x² j and S is the graph of - ža (1+æ²…

A: Here, Fx,y,z=y2i+3x2jz=121+x2-y2

Q: Find the value of the integral fs (V x A). da if the vector A = yi + zj + xk and Sis the surface…

A: Given the vector A=yi+zj+xk and S is the surface defined by the paraboloid z=1-x2-y2

Q: 2. Use a parametrization to express the area of the given surface as a double integral and then…

A:

Q: Evaluate the surface integral. z2 S is the part of the paraboloid x = y2 + z² given by 0 sx 5 4 1 V5…

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Q: Prove that the integral of the bottom of a half ellipsoid, (x/a)^2 + (y/b)^2 + (z/c)^2 =1, is equal…

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Q: Use cylindrical coordinates to evaluate the triple integral □ لاا √² + y²dV, where E is the solid…

A:

Q: 4. Let S be the portion of the paraboloid z = 4 – x² – y? in the first octant. (a) Evaluate the…

A:

Q: Evaluate the triple integral ||//. z°e" dV where E is bounded by the parabolic cylinder z = 16 – y?…

A: The volume of a solid can be calculated using the triple integrals. The unit dV can be written as…

Q: 1. Use a parametrization to express the area of the given surface as a double integral and then…

A:

Q: use a parametrization to find the flux ∬S F . n dδacross the surface in the specified direction. F =…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: use a parametrization to find the flux ∬S F . n dδacross the surface in the specified direction. F =…

A:

Q: Use cylindrical coordinates to evaluate the triple integral |||| Væ² +y² dV, where E is the solid…

A: Mentioned below is the answer

Q: . Calculate the flux integral fF.n ds, where C is the positively oriented circle of radius 1…

A: Given function is, Fx,y=x,2y The formula for calculating the flux of the integral ∮F·nds is,…

Q: 3. Consider A(r) = (y, -x,0), and the line integral A• dr along the C boundary of the plane x + y +…

A: The given vector function is A(r)=(y,-x,0)., the line integral ∮CA·dr is along the boundary of the…

Q: Suppose f(x, y, z) = x² + y² + z? and W is the solid cylinder with height 9 and base radius 5 that…

A:

Q: Evaluate the surface integral SP ( – 2) // where S is the portion of the cylinder r2+22 = 1 above…

A: It is given that S is the portion of the cylinder x2+z2=1 above the xy plane between y=1 and y=2.

Q: 1.Let D=6xy ax+ 2(xz+3z2)ay+3yz az C/m2.Evaluate the surface integrals to find the total charge…

A:

Q: 1. Use a parametrization to express the area of the given surface as a double integral and then…

A: Here we will cylindrical co ordinate system to parametrize the surface  x=r cosθ , y = r sinθ , z=z

Q: 3. Calculate the volume of the closed body formed with the surfaces; "y?+ (z-1)? = 1, x=2 and x+z=5"…

A:

Q: There is a curve parametrized by x = 3t, y = 2t°, 0<t an equation for this curve in terms of ne…

A: Here we have,

Q: Evaluate the integral // Fn ds where F = (2r+32)i-(rz+y)3+(y² +2)& and S is the surface of the…

A:

Q: Let f(x, y, z) = In (x² + y + z?). The level surface f (x, y, z) = In 4 is a: Elliptical cone around…

A: Given  f (x,y,z) = ln( x2+ y+z2),To find : level surface f= ln4

Q: Determine the element of surface area dS in the special case of the paraboloid of revolution z = x2…

A:

Q: Calculate the points of intersection of the curves x² = 4y and bn=) = y 29vaus at newed biloa gris 1…

A: Centroid: The centroid or centre of mass of a region bounded by the curves is the point where the…

Q: 2. Use a parametrization to express the area of the given surface as a double integral and then…

A: Given ,x2+y2+z2 = 22       _________(I)and z = x2+y2     __________(II)Putting the value of z from…

Q: Use Stoke's Theorem to evaluate the line integral / 7ydx + 3zdy + dz where C is the intersection of…

A: Use Stoke's Theorem to evaluate the line integral ∫C7y dx+3z dy+ dz, where C is the intersection of…

Q: Find the centroid of the solid bounded by the parabolic cylinder 1- y? and the three planes given…

A: To find the centroid of the solid bounded by the parabolic cylinder: The region is defined as…

Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 8x + 16y + 24z on the elipse…

A: To determine the maxima and minima of the function f(x, y, z) with respect to the function is…

Q: According to the divergence theorem, what is the integral that represents the surface integral of…

A: The divergence theorem is very significant in evaluation of surface integral through volume…

Q: (a) Compute the surface integral || a xy dS, where S is the quarter cylinder x2 + y? = 1; x, y > 0…

A: Given that The surface integral is ∬Sxy dS, where S is the quarter cylinder x2+y2=1; x,y≥0 between…

Q: (a) Compute the surface integral || xy dS, where S is the quarter cylinder x? + y? = 1; x, y > 0…

A:

Q: 2. Compute the scalar line integral xy ds where C is the part of the circle of radius 2, centered at…

A: Put x=2cost , y=2sint

Q: Use Stokes' theorem to evaluate line integral (z dx + x dy + y dz), where C is a triangle with…

A: Consider the provided question, We have to evaluate the given integral by using the stokes theorem,…

Q: b) Use the Gauss-divergence Theorem to find the surface integral ff, F.n ds, where S is cylinder x²…

A: As stated in question we will use Gauss-divergence Theorem to solve this question.

Q: Use Stokes' theorem to calculate (V × A) · ndS with A = 3yi – xzj+ yz²k, where S is the surface of…

A:

Q: Sketch the reglons enclosed by the glven curves. y = Vx, y= X= 16 y y 6 4 4 3 3 2 10 15 10 15 O-1…

A: Given : y = √x  y = 1/3 x  x = 16

Q: 1. Use a parametrization to express the area of the given surface as a double integral and then…

A: