Compute the integral |(5y + pz2020, ) dx + (19x – e-4ycos(v) sin y) dy over the portion of the circle x² + y² = 4 in the upper half plane.

Q: 3) Evaluate the iterated integral by converting the to polar coordinates -√₂x-x² a) √²ty² dydx…

A: Given that, The integrated integral: (a) ∫02∫02x-x2x2+y2dydx,  such that , the region is…

Q: 1.5 3-y QI) Evaluate the integral dx dy using polar coordinate

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Q: Q2: I| (x? +y?) dxdy a) Use the polar coordinate to find the integral 0 0 1/16 1/2 b) By using the…

A: In the given question we have to find the integral value of the function.

Q: 1 (x+y')* dy dx -J3X 2

A: Double integration of function gives the area under the function curve. Double integration can be…

Q: 4. Evaluate √² +² dzdy by changing to polar coordinates. Sketch the region of integration..

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Q: Find : ( 39 - Sincm) dx +(2x*) dy when C is the boundary of the limited area by curvess y= e* and in…

A: Given that I=∫c3y-sin x dx+2x2 dy                                   ……(1)   Boundary is given as…

Q: Qz/ Evaluate the complex integral: dz (z+ 1)(z – 2) where C is: a) The circle Iz] = 3 b) The circle…

A: Note:- If z =(x+i y)  then z =x2+y2 Cauchy's Residue Theorem:- ∮Cfz dz =2πi sum of residue   Given…

Q: Find the arclength of y = 2a + 4 on 0 < a < 4

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Q: Compute the line integral -xdy + ydx 2(x-y)2 + 4xy where L is the circle (1-x)2 + y? 3 with a…

A: We will find parametric equation of L and then convert whole equation in parametric form

Q: -dz Q5/ (A) Find the value of the integral 3 where C is the circle z+2 = z(z+1)"*1

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Q: Find (d^2)y/d(x^2) at t= pi/3 for the parametric curve given below. Write your final answer in the…

A: Given parametric curve, x = t+sin(t) y = t-cos(t)

Q: (c) . sin (92? +4y?) dA D where D is the region in the first quadrant bounded by the ellipse 9a?…

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Q: +6x=4y-y². Find the area inside the conic x² +

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Q: Let X = {1, 3, 5} and Y = {a,b,c,d}. Define g: X→ Y as follows: 1 b, 3 → b, 5 → b. inverse image of…

A: For a function: y=f(x), the set of real values of x for which f(x) is defined is called the domain…

Q: (a) Let f(z) = 1 - 2i)(24 – 23) - 2 Using CRT, evaluate the integral Of(2)dz, where the contour C is…

A: 1. The point z=a is said to be an isolated singularity if there exists a number such that f(z) is…

Q: QI) Evaluate the integral dx dy using polar coordinate

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Q: 2 9-x sin (x? +y² ) dy dx 2 sin x +y 2 9-x 3.

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Q: Find the arclength of y = 4x² - 2 on 0 ≤ ≤ 2

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Q: Let F = (3z + 3x²) ¿+ (6y + 4z + 4 sin(y²)) 3+ (3x + 4y + 6e²²) k (a) Find curl F. curl F - (b) What…

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Q: (a) Let f(2) = 24 +5z3 Evaluate the integral f(2)dz, where the contour C is the circle k| = 2.

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Q: (1) Find the area of the curved surface of the upper half of the sphere x2 + y² + z² = a²(a > 0) on…

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