Question 2. Use Green's Theorem to evaluate f, 2y?dx + 5xydy, where C is the boundary of the semi-annular region D in the upper half-plane between the circles x2 + y? = 1 and x? + y² = 4.

Q: A curve C is the boundary of a shaded region D which defined by y = 2x-4 and y = 2x in…

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Q: Let C be the boundary of the portion of the plane x+y+z=2 that lies in the first octant, oriented…

A: It is a 3D and we have to draw in a sheet which is 2D. I is a tough task but I will try to draw it…

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

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Q: Apply Green's Theorem to evaluate the integral. $(7y + x)dx + (y + 9x)dy C: The circle (x-3)² +…

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Q: Verify: Green's theorem in the plane for f(2x-y³) dx-xydy, where C is the boundary of the region…

A: Given information ∫c2x-y3dx-xydy Here, C is the boundary of the region enclosed by the circle…

Q: QUESTION 6 Use the Green's Theorem to evaluate the line integral xfydx +xy dy. where C is the…

A: Using the given vertices we can draw the required triangle and then apply Green's theorem to…

Q: 9. It is recommended that you use polar Evaluate ffe (3x + 2y) dà where Ris the region in the upper…

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Q: Use Green's Theorem to evaluate Se (y? – tan-1 (r)) dr + (3r + sin (y)) dy, where C is the boundary…

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

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: 28. F(x, y, z) = x³i+y°j+z°k, and S is the sphere of radius 3 and centered at the origin.

A: divF→=ddxx3+ddyy3+ddzz3        =3x2+3y2+3z2        =3x2+y2+z2  by divergence theorem,…

Q: Can you show the steps on how to do this integral?

A: Consider the provided question, (3) Evaluate the integral by using the greens theorem,

Q: 3.use Greens theorem S(1+x dx + 2xy dy ,where C is triangle With vertices (0,0),(1,0).(1,3) oriented…

A: "Since, you have asked multiple questions, we'll solve the first question for you. If you want any…

Q: Question 5 Find the surface area of that portion of the surface z = V4 -x that lies above the…

A: Option (B) is correct

Q: 19. If R is the region enclosed by a simple closed positively-oriented curve C, then the area of R…

A: Given that if R is the region enclosed by a simple closed positively oriented curve C . We need to…

Q: Consider the region R bounded by the parabolas y = and y = r - 3.r, as depicted in the graph below.

A: Since you have posted multiple questions but according to guidelines, we will solve the first…

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: How do I evaluate this?

A: Let C be the quarter circle centered at (2,0) that goes from (1,0) to (2,1).

Q: Which of the following correctly represents the plane region in the first quadrant bounded by the…

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Q: (a) Let f(z) = 4 + 5z3 Evaluate the integral Of(z)dz, where the contour C is the circle z| = 2. C

A: So here we will find integral by residue theorem.

Q: Question 4 Use polar coordinates to compute the double integral of f(r, y) = ea+y°)/² on the region…

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Q: 25. Figure 21 shows the region enclosed by r y- 26y + 10 and r = 40 – 6y?-y. Match the equations…

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Q: Question L. Evaluate the following Sffela?+y+2y"dv, where Q is bounded by the hemisphere z = 4-x2-…

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Q: The tangent plane to the graph of the surface z=in(x2+y?} at the point (1,0,0) contains point…

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Q: 6. Compute the contour integral (a) / COS Z -dz where C is the positively oriented circle |z – 1| =…

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Q: - 2 and Evaluate || curl(F)·dS where S is the portion of the top half of the sphere x +y +z? = 4…

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Q: The area of the region bounded by the curves x = y2 +1 and y = x -3 is 2 -1 16 (A) 17 (C) 3 (D) 4 13…

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Q: (a) Let f(z) = (z + 4 - i) (z4 + 5z®) Using CRT, evaluate the integral Of(2)dz, )dz, where the…

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Q: Question 18 Find the surface area of that portion of the surface 2 = V4 -x that lies above the…

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Q: Apply Green's Theorem to evaluate the integral. Py + x)dx + (y + 3x)dy C: The circle (x- 3)? + (y –…

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Q: Question 20 Set up the integral that calculates the area of the region enclosed by the circle x2 + y…

A: The relation between polar coordinates and Cartesian coordinates is given by . Area bounded…

Q: Find the integral fc ez dz where C is the circle |z| = 3 in CCD. (z – 1)2(z – 2) %3D -

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Q: 9. Using Stoke's Theorem Evaluate [(2x – y)dx – yz dy – y zdz) where c is the circle x +y =1,…

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Q: (b) Consider F(x, y) = -i+ j, where (x, y) # (0, 0). x²+y2 x2+y2- Without using Green's Theorem,…

A: Consider the provided function,

Q: Find the area under the curve for the parametric function defined by the equations x(t) = 5t, y(t) =…

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Q: (a) Let f(z) = %3D (z + 4- i) (z4 + 5z³) Using CRT, evaluate the integral Of(2)dz, where the contour…

A: In the given question we have to evaluate the integral                               where the…

Q: Find the area of the plane z = 4x+y for all (x,y) ∈ R where R is the region in the first quadrant…

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Q: Evaluate the line integral G. dr with G(x, y) = xyi+ 2y² j, and C is the closed path comprising the…

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Q: Question 3: Find the area of the surface portion z = x* + y* Which is below the plane z-9|

A: To find the surface area of the portion of the below surface that is below the plane z = 9. z=x2+y2

Q: The tangent plane to the graph of the surface z-In(x<+y) at the point (1,0,0) contains point (3,3,t)…

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Q: B. Let C be the curve y = 1 – x2, 0< x < 1. If C is rotated about the y axis find the area of the…

A: our objective is to calculate the surface area.

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: Using Green's Theorem, evaluate the line integral |(-*y)dr + ay*dy re C is the circle a2 + y? = 1…

A: Let C is a counterclockwise oriented simple closed curve with the interior region R. According to…

Q: Q-3 If R is a closed bounded region in the xy-plane whose boundary curve is C with arc lengths and…

A: Given R is a closed bounded region in the XY plane whose boundary curve is C with arc length s  and…

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: Sketch the regions enclosed by the given curves. y = Vx, y = Ex, x = 9 y y 5 5 4 3 3 1 1 X 2 4 6 8…

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Q: Use polar coordinates to evaluate S (5x-y) dA gion in the fourth quadrant bounded by the circles nd…

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Q: Which of the following is the equation of the tangent plane to the surface z=x2 - x+3y² +y at the…

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Q: 2. Use polar coordinates to evaluate If y² dA, R where R is the region bounded by the line y = x,…

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Q: Evaluate y dx+3xy dy, where C is the boundary of the semiannual region D in the upper half-plane…

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