Q10// Evaluate S. curl F dS where F 2yi - xj + xzk and S is the surface x? + y? + z? = 4 where z > 0

Q: Use Green's Theorem to evaluate the line integral ∫c ( x − y ) dx + ( x + y ) dy where C is the…

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Q: B- Find all local extreme values of the following surface. f(x, y) = 2xy – x² – 2y? + 3x + 4.

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Q: 2e Let f (2) Let C be the circle (z – 4) (z – 6) z = 8 in the counter-clockwise direction. - - Find…

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Q: 5) Let S be a surface composed of the union of the surfaces S1 and S2 with equations S1: 4z + x? =…

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Q: Q10// Evaluate J, curl F dS where F = 2yi – xj + xzk and S is the surface x? + y2 + z2 = 4 where z >…

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Q: F = 2yj+z k and S is the surface y? + z? = 4 between x 0 and x = 3 – z. Compute SL.F.ds

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Q: Integrate f(x, y, z)= -√√x²+² over the circle r(t)=(acost)j + (asint)k, 0≤t≤2.

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Q: The area of the surface formed by revolving the graph of x = /ỹ on [2,9] about the x-axis is given…

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Q: find the surface about the X-axis for OsX L 2 by revolveng u= X area create d

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Q: ix of F across the surface defined by R(u, v) = (2u, 3v E [0, 1].

A: We have to find the flux according to the given information

Q: The surface area of the surface generated by revolving y= 1 – x² for 0<x<1 about the x – axis is s=…

A: The solution is as follows

Q: 3. Evaluate , (x + z)dS where the surface S is the first-octant portion of the cylinder y² + z² = 9…

A: Step:- 1 Since, we know Surface integrals ∫∫Sf(x,y,z)dS=∫∫Df(x,θ) rx×rθ dxdθ…

Q: b. Evaluate the line integral ycos(xy)dx +(xcos(xy)+x)dy where R is the circle x'+y =9 traversed…

A: Solution Given b). ∫y cos(xy)dx+(xcos(xy)+x3) dyevaluate the line integral

Q: The surface area of the surface generated by revolving y=1-x? for 0<x<1 about the x- axis is None s=…

A: surface area S =∫012πy.ds where ds=1+(dy/dx)2

Q: An integral expression for the area of the surface generated by rotating the curve y=√x, 0≤x≤ 1…

A: Given: y=x3, 0≤x≤1 To find the area of the surface generated by rotating curve y=x3 and 0≤x≤1 about…

Q: z+2 19.7-42+42 dz where C is the circle z-2|= 1. Evaluate the integral

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Q: Q11// Evaluate grad V dS where V = x + y? + z? and S is the surface x2 + y2 = 4 bounded by z=0,z=4…

A: To Determine :-  The ∫S grad V dS where V = x + y2 + z2 and S is the surface x2 + y2 = 4 bounded by…

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve 5y³ dx -…

A: We know that , Green's theorem ,  Consider C be a positively oriented  , simple , closed , piecewise…

Q: 2 3 3 Find the area of the surface z = = X2 + y2 3 where 0 < x 1, 0 < y < 1

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Q: Solve the following surface integral (use definition): F = [322 6 6rz] with parabolic cylinder…

A: To calculate the surface integral of the vector field F across the surface S, use the following…

Q: Q10// Evaluate S, curl F dS where F = 2yi – xj + xzk and S is the surface x2 + y? + z2 = 4 where z>…

A: Given integral is∫Scurl F dSwhere F=2yi-xj+xzkand S is the surface x2+y2+z2=4 where z&gt;0

Q: Use Green's Theorem to evaluate the integral (x² - y)dax + 3xdy where C is the circle x² + y² = 1…

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Q: An integral expression for the area of the surface generated by rotating the curve X =Vy , 1sys8…

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Q: Find the surface arca of y = (1/3)r 10<x <1 revolved about the z-ax

A: Given: The equation is y = 13x3 , 0 ≤x≤1 revolved about the x - axis.

Q: 5 Evaluate F.ds over the surface S defined by x² + y² + z² = 4 for z ≥ 0 and bounded by x = 0, y =…

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Q: 17. Evaluate the integral: S, 9x? – 6dx. 18.Determine the center of the circle x² +y² = 25. %3D

A: (17)  Given that I=∫-159x2-6 dx It is known that ∫xndx=xn+1n+1 So, I=9x33-6x-15 =3x3-6x-15 Now we…

Q: Use Green's Theorem to determine the value of the following line integral 1 I - (7 x + 3 y ) dx + (…

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Q: find the area of the surface generated when the given is revolved about the given axis y = 8√x, for…

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Q: 4. Evaluate the line integral / r y* ds where C is the right half of the circle r² + y² = 16.

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Q: Q4 Evaluate where F = xi – yj+(x+y+z)k and C is the boundary of the surface z =1,0<x,y <1.

A: The given problem is to evalute  the surface integral of vector field over given boundary of surface…

Q: Q10// Evaluate S, curl F dS where F 2yi - xj + xzk and S is the surface x2 + y? + z? = 4 where z > 0

A: Given that

Q: Find the area of the surface f(x,v)= 2 +12x + y over the domain bounded by the x-axis and the…

A: To find the area of a surface, do the following  Draw the region in a plane and shaded that region…

Q: Q3// Evaluate F dS where F = xi + yj + zk and S is the surface x² + y? = 9_ in the first two octant…

A: Given F=x,y,z and S:x2+y2=9 in the first two octants bounded by the planes z=0 to z=2 and y=0.…

Q: Q7. Use Green's theorem to evaluate fy² dx + 3xy dy, where c is the boundary of the semi annular…

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Q: Q7. Use Green's theorem to evaluate y² dx + 3xy dy, where c is the boundary o the semi annular…

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Q: Evaluote the live integral | (xZ+ y) ds along the curve c defined byき)=くターも,スセt,-スモ> ON Osts I -21…

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Q: 2) Find the area of the surface r(u,v)=u cos vi+u sin vj+2vk where 0su<3 and 0<vs 2n .

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Q: Q4 Evaluate [F•ds where F = xỉ – yj+(x+y+z)k and C is the boundary of the surface z =1,0<x,y <1.

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

Q: (3z+1) z'e (b) $1+2 z'e² (a) p- - dz -dz 3 (s + z7)(1– z)z?

A: Evaluate the given two integrals over the circle z=4 (a) Let fz=3z+12zz-12z+5 The singularities of…

Q: Let C be the curve y = 4√√x for 2.1 ≤ x ≤ 4.8. 8 7 5 4 3 2 1 2 3 4 Find the surface area of…

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Q: Which of the following provides the curve of intersection = 14? of the surfaces z = √√√x² + y² and…

A: We have to find the curve of intersection of the surfaces  z=x2+y2  and  x2+y2+z2=14.

Q: 3z2+z+1 Q4. (a) Evaluate using Cauchy's integral formula Sc (z2–1)(z+3) dz where C is the circle |z|…

A: The given problem is to evaluate the given complex integral over the given region using cauchy…

Q: #3. Evaluate the line integral O (y dx- x dy) where C is the positively oriented circle with center…

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Q: (a) Let f(z) = 24 + 5z3' Evaluate the integral f(z)dz, dz, where the contour C is the circle |z| =…

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Q: What value of z in the interval 0< z< 2 corresponds to the greatest magnitude of Curl(F) where F(x,…

A: Given: F→(x,y,z)=tan(x),y4,2xcos(z-1)

Q: Q2 Find the maXimum and minimum values of aFunction FCXS.2) = 8x+j+ 2 en the Surface x+y, z"=18 %3D

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Q: 3. (a) Use Green's theorem to evaluate the line integral 4 y* dx – a* dy where C is the positively…

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Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. 2y3 dx…

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Q: Q3// Evaluate ſ. F dS where F = xi + yj + zk and S is the surface x? + y? = 9_in the first two…

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Q: ii) Find the exact area of the surface obtained by rotating the curve y = x³ + 1 ≤ x ≤ 2, 1 3 12x 9

A: Use Area of surface  formula.