soùd lines For Portions dash ùnes of borndry included in thee bmain and not include Suot1 For d) F(xリ)ン Jx ty tz e) FCX! y)= I lnzy x-2

Q: 1. Let S be the part of the cone z? = x? +y² that lies between the planes z = 1 and z = 2. Compute…

A:

Q: 1. Use the Stoke's Theorem to evaluate y'dx + xy dy + xz dz, C where C is the bounding curve of the…

A:

Q: Compute the line integral (Баллов: 2) Jo ds, Cis the right half of circle x2 + y 16 (counter…

A:

Q: a) Consider the following line integral (rdr + ydy + (rz – y)dz) along a curve C given by r = ti+…

A:

Q: ?) Evaluate CC xdv where E the bounded where E is Hhe bounded 2 by the para bo loid *=4yt 42 and yhe…

A: We have to evaluate the value of ∫∬Exdv,where E is bounded by the paraboloid x=4y2+4z2 and plane…

Q: Consider the solid that is bounded above by x² + y? + z? = 169 and below by z=5. %3D

A: In this question, we have to write the triple integral to find the volume of the solid bounded by…

Q: Evaluate ſſ, Vy² – x² dA where boundary of R is the parallelogram bounded by the four lines

A: In this question, we evaluate the double integral by using the change of variable. The region is…

Q: Use Green's theorem to evaluate O(1-y') dx+(x³ +e" ) dy , where C is the boundary of the region…

A: The integral is ∮C1-y3dx+x3+ey2dy where C is the boundary of the region between the circles x2+y2=4…

Q: S how that the line af intesection of the Planes and 5x-2y-Z=0 X+2y-22= 5 is Paralkel to thelime メ+3…

A:

Q: Let f (z) = 33O = Q A = 10and B= 10 + 10iet C be the contour composed of the line segments OAand…

A: The given problem is to evaluate the complex integral of the given function over the given semi…

Q: If C is the line segment from (1, 3) to, (0, 0), find the value of the line integral: So(3y² i +3xj)…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Evaluate the line integral xyld x + (x²+y)dy] +. where c is the saruare farmed by the lines

A: Let us consider a line integral ∫CP dx+Qdy then it can be written as  ∫D∫∂Q∂x-∂P∂y dA  Where, P and…

Q: Let NR be a disc with centrum in origo and radius, R. 1 Assume that, J(x, y) x² + y? < R². 1+x2 + y²…

A: ΩR be a disk with centrum in origo and with radius, R. Assume that, Jx,y=11+x2+y2,x2+y2≤R2. Then we…

Q: Evaluate the line integral So 7y dr + 3x dy where C is the straight line path from (2, la 7uda + 3z…

A: Introduction: A line integral is an integral that determines the function to be integrated along a…

Q: WX || ZY and Zs Z and Y are supplementary WXYZ is a parallelogram Given: Prove: W Y

A: It is given that,  WX ¯|| ZY¯  and ∠Z and ∠Y are supplementary To prove :- WXYZ is a parallelogram

Q: Show that T(u, v) = (u² – v², 2uv) maps the triangle = {(u, v) : 0 < v < u < 5} to the domain D…

A:

Q: Use Stoke's theorem to evaluate // curlF - dS where F(x, y, z) = 2y i+ 3xj + (z – x) k and S is the…

A: The given integral is∫∫CcurlF→·dSwhere F→x,y,z=2yi^+3xj^+z-xk ^and S is theportion of y=11-3x2-3z2…

Q: c) By using Green's theorem, evaluate (In (r) + ry – y²) dx + (e" +x²y - 3ry) dy, where C is the…

A: Green's therorem establishes relationship between double integral and line integral. Double integral…

Q: Jo xy ds where C is the line segment from (2,0) to (5, 4). Evaluate the line integral

A:

Q: Let C be the positively oriented circle x? + y? = 1. Use Green's Theorem to evaluate the line…

A: Given : C is a positively oriented circle x2+y2=1 We have to evaluate the line integral…

Q: By making an appropriate change of variables, evaluate the double integral = (x + y)e*-Y dxdy where…

A:

Q: If the region R is bounded between two circles 961 x² + y? = 4, x² + y? then we have: 2л 3 sin(Vx2 +…

A:

Q: Let d: RxR-R, defined as d(z, y) = |r|, then d is metric O not metric because d not sats fied d (r,…

A:

Q: O By using Green's theorem, evaluate $ (In (2²) + æy² – y²) dæ + (ev + x²y – 3ry) dy, where C is the…

A:

Q: 12. Evaluate by using Stoke's Theorem [sin z de - cos x dy + sin y dz] where C is the boundary of…

A:

Q: ded above by surface z = 10 – x2, bou e planes y = 0 and y = 3.

A:

Q: F. dr = 0 for every closed curve Cin R, an open connected region. %3D True O False

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

Q: Use Stoke 's Theorem to evaluate [ V. dr, where v= y²i + xyj + xzk, and c is the bounding curve of…

A:

Q: se the Divergenci Theored tobevaluhbe Sis the bSH cordinate planes whe re bounded end the planess…

A:

Q: Compute where h(s) = rs? -r. Assume r is a constant. %3D ds

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: A solld is obtained by rotating the shaded reglon about the specifled line. about the x-axis y y = V…

A: The given surface are y=x and y=20-x. The area between the two surfaces is obtained by ∬dx dy.

Q: 6- Evaluate the line integral fF - dr, where F = [ry, yz, xz] and C is the boundary of the…

A:

Q: 3. Evaluate ox?y dx + xy? dy using Green's y 2 Theorem, where C is positively oriented by line y =x…

A:

Q: If the region R is bounded between two circles x² + y = 4, x² + y = 9, then we have: sin(Vx2 + y?)…

A:

Q: WY = WZ bail M is the midpoint 40. Given: of YZ MX 1 WY MT 1 Zojpib tisz ow Prove: MX = MT 41.)…

A:

Q: 11. Let F(r, y) = (ry', yr') and let C be the boundary of unit square: 0 Ss 1, 0< yS1. Use Green's…

A: That's easy. Have a great day!!!

Q: Use Green's Theorem to evaluate (1in z – 2y) dz + (x – ycos y) dy, where C is the circle (x – 4)² +…

A: Given: C is the circle x-42+y-42=9. ∮Cxsinx-2ydx+x-ycosydy. To find: Using Green's theorem, value…

Q: 5. Show that the equation of the tangent plane to f(r, y, z) = c at (ro, Yo: 20) is given by the…

A: This is the question from vectors.

Q: B is the first quadrant part of the region enclosed by the circles x2 + y? = a? and x2 + y? = b2…

A:

Q: two x' dA, where R isa Regian bounded by fufcirck xye 1- x"rye-a' and x ty?=b² 2 SS(x*yj*dA, whera R…

A: Note that this is a multipart question, so as per the company policy, we can solve only the first…

Q: . SS, xcos(y)dA, D is bounded by y = 0,y = x² ,x = 1.

A: See the details solution in below

Q: Evaluate the line integral Levis where C is the half circle x² + y² = 1, y ≥ 0. x² + y² ds

A:

Q: a) Evaluate the line integral S. (2x - y) dx – (x + 3y) dy, where C is a straight line from (1,1) to…

A:

Q: the line integral SexY² ds where C is the of the Circle x² + y²=4 oriented clockwise Evaluate Cight…

A:

Q: Solve the fAllowing equetiun by cepuration of warnoble methal xQu-y Du t Zy = X Y glven uli,1)= 3…

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: Evaluate the line integral: x dy – y da x² + y² where C is the circle x² + y? = a², a > 0, oriented…

A: