Please evaluate P (3y – esin(@)) dx + (7x + Vyª + 1) dy, - where C is the circle x2 + y? = 9. Hint: use Green's Theorem!

Q: Determine a∈R such that ∫CF⋅dr = −2−(3π/4), where F (x, y) = (ay, (x^2 − y)/2) and C is the part…

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Q: .2 Use Green's Theorem to evaluate x-ydx - xy² dy , where C is the circle x +y² = 9 with…

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Q: 5. Let C be the circle x +y} =4_which is positively oriented. Let C, be the upper half-circle C1 =…

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Q: Let YR be the circle of radius R with counter clockwise orientation. Prove that 2 – 1 - lim R00 YR…

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Q: Q2 Calculate 8- z dz, z(4 - z) where C is the circle of radius 7, centre 0, negatively oriented.

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Q: Verify greens theorem form 1 for F=x^3i+yj and c is the circle x^2+y^2=1, oriented anti clockwise

A: Find ∫CFdr, the line integral of F, where C is the circle x2+y2=1, oriented anti clock wise…

Q: Use Green's Theorem to find SF ·dř where F = (y³, –x³) and C is the circle x² + y² = 3. %3D %3D

A: The given vector is  F = y3i - x3j

Q: Show that [(x- y) dx + (x – y)' dy] = 3ra" taken along the circle x +y =a° in C the counter…

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Q: 2. Evaluateſ. a+ (z+30:) dz along C which is the circle |z + 3i| = 3, counterclockwise. %3D (z+3i)

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Q: Set up and simplify (but do not evaluate) : 3x ds, where C is the arc of the circle r2 + y² = 4 from…

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Q: .If C is the circle (traversed once counterclockwise) of radius 2 with center at z = 0, %3D 7e?…

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Q: Evaluate the line integral 3xy® ds, where C is the right half of the circle x? + y? = 36.

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Q: Verify Green's Theorem where F1=y^2-7y , F2=2xy+2x and the curve C is a circle x^2+y^2=1

A: Given: F1=y2-7y , F2=2xy+2x and C is a circle i.e., x2+y2=1 As, we have:…

Q: 4. Let C denote the circle |z – 2i| = 1, taken in the usual counterclockwise orientation. Compute by…

A: Given: Let C  denote the circle z-2i=1 z-2i=1x+iy-2i=1x+iy-2=1 So, Centre of circle will be 0,2 and…

Q: Evaluate the double integral 1+ 4x² + 43²&A where D is the bottom half of the circle x? + y? = 16.…

A: In polar coordinates,                                   and

Q: Use Green's Theorem to find (8y + x) dx + (y + 2x) dy, where C: The circle (x - 4)2 + (y-3)2 9 541…

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Q: Q2 Calculate 8-z dz, z(4-z) where C is the circle of radius 7, centre 0, negatively oriented.

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Q: Use Green's Theorem to evaluate the integral (3x² – y)dx + 3xdy where C is the circle a? + y? = 1…

A: As we know from the Green's theorem; ∫CMdx+Ndy=∫∫D∂N∂x-∂M∂ydA   Given; I=∫C3x2-ydx+3xdy So, M=3x2-y…

Q: 3 Use Green's theorem to evaluate [x³y dx - xy²dy, where C C is the unit circle x²+y=1 with…

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Q: 2: Evaluate O (6y+x)dx+(y+2x)dy where C is the circle (x–2)²+(y-3)² = 4 | a) Using Green's Theorem

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Q: 6. Let C C R? be the positively-oriented boundary of the graph of the circle x2 + y? = 1. Using…

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Q: O Evaluate + z )ds where C is the circle F(E) = for 0EEE Zo

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Q: Please evaluate (3y – ein(e) dx + (7x + Vy* + 1) dy, where C is the circle a? + y = 9. Hint: use…

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Q: Integrate counterclockwise around the circle |z – 6i| = 3. z(z – li)? - NOTE: Enter the exact…

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Q: Find a parametric description for the circle x2+y2-6y=0, oriented clockwise and where t begins at 0.…

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Q: Please evaluate (3y – einl2) dr + (7x + V yt + 1) dy, where C is the circle x² + y² = 9. Hint: use…

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Q: Evaluate  ∫C (3y + exsinx) dx + (8x - ln(y3+2)) dy, where C is the circle x2 + y2 = 9  with positive…

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Q: Ex: Fmd the lengthoftre arc af the Circle with P.R. ret)= [acest from Co,0 to asiut] o Ofa),- %3D

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Q: 6. Prove (by plot) the equation (x²+y²=16) is the circle in 2D , and cylindrical in 3D.

A: We will answer the first question since we don't answer multiple questions at a time. Please…

Q: zt e dz if t>0 and C is the circle z]=2. Evaluate 2ni C 2πίz+1

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Q: 12. Use Greens Theorem to calculate P y'dx -a'dy C where C consists of the arcs y=x² and y =x1/2,…

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Q: 2. Use Green's Theorem to evaluate (7z +y) dy - (r² – 2y) dz where C is are the two circles as shown…

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Q: 17. Evaluate OF . • dr where C is the circle x +y² = 1, z = 0 and F=yi+zj +xk.

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Q: Use Cauchy's Integral Theorem to evaluate fr 12z-3(2-42 dz where I' is the circle |z| = 2 described…

A: Given ∫ez2z−3z−42dzWe know the formula ∫fzz−an=2πin−1!fn−1aWhere 'a' is pole of order nGiven region…

Q: Use Green's theorem to evaluate $ 2y3 dx – x3y² dy, where C is the positively oriented circle of…

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Q: 4. Let C be the the circle ² + y² = 4 and Calculate the work(W = [,F dr when C is traversed in the…

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Q: ⒸFind S (x- y²) dA, where I is bounded by the circle of D center (0,0) and radius 2.

A: As per as our guidelines i am supposed to answer

Q: Use Green's Theorem to evaluate - – In(x² + y²))dx + 2 tan¬²(y/x) dy, C is the circle (x - 4)² + (y…

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Q: 6. Compute G.T ds if K is the portion of the circle x2 + y* = 7 in the third quadrant (oriented…

A: region of integration is part of circle, x2+y2=7, lying in 3rd quadrant, thus, limits of x,y are -7…

Q: By using Cauchy's integral formulas evaluate sin Tz2 + cos TZ² dz (z + 1)(z – 2) C and e2z dz (z –…

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Q: 2. Use Green's theorem to evaluate fe e-x³ dx + (5x + sin(y²)) dy, where C is the circle x² + y² = 4…

A: Please see the below picture for detailed solution.

Q: z+i dz , where T is the circle Iz – 3i| = 1 traversed once (2) Compute counterclockwise.

A: The general form of a complex number is given by z=x+iy, where x,y are two real numbers and i=-1.…

Q: Find the upper bound of |[∫c ez^2 + 1 / (z - 1)2 + 5] dz|, where C is the circle |z - 1| = 2.

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Q: Verify Green's Theorem in the plane for F = -3y³i+ (3x3 + cos y)j where C is the circle x2 + y? =…

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Q: dz b) C: z|= 4 is a circle calculate the integral .(z-1)(z² +9)

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Q: Express you answer in Mdx + Ndy = 0. 1. Circles whose center is passing through y = 4x %3D

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Q: 9. Determine the image of the circle z +- 2 P 1 2 3i under w(z) ==+l+i. Z

A: Note: Hi! Thank you for your question. As per the guideline we can solve one question at a time in…

Q: The DE for the family of circles of radius 9 is: A [1+ (y')²]³– 81=0 B [1+ (y')²]²- (» )²-[1+…

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Q: Let YR be the circle of radius R with counter clockwise orientation. Prove that 1 -dz = 0. lim z3 +…

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Q: Let C be the circle |z| = 4 traversed once in the positive sense (counter %3D clockwise). Compute :…

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