The value of the integral (inage 1). where C is the closed curve 4x2 + 5y2= 7, 3x + 2y − 9z = 5.

Q: Complete integral of the equation z = px+ qy – 2pq is, (a) z = ax+ by – Vab (b) z = ax+by + Vab (c)…

A: Clairaut's form is given by z = px+qy+f(p,q) Its complete integral is given by z = ax+by+f(a,b)

Q: By making an appropriate change of variables, evaluate the double integral I - [[ (7 + v)e=" »° dzdy…

A: By making an appropriate change of variables, evaluate the double integralI=∬R(x+y)ex2−y2dxdywhere R…

Q: 2. Find an upper bound of the absolute value of the integral e + 1 (a) dz, where C is the right half…

A: We know that : Imz=12z-zi . Therefore, ∫Cz2-Im(z)dz=∫02+2iz2-i2z-zdz.

Q: 2- Show that the function is analytic everywhere except at the points z +i += and on the half line…

A: The region where a complex valued function is analytic is actually its domain of definition. A…

Q: Convert the integral  0∫2 0∫2z y∫2y dxdydz in the order a) dzdxdy b) dxdzdy

A: Given: ∫02∫02z∫y2ydxdydz

Q: The area of the region bounded by the curves 2y2 +2 and z 2y+2 is 2. 3 5 -1 -2 16 17 (A) 3 (B) 3 13…

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Q: 6- Evaluate the line integral fe F dr, where F = [ry, yz, r2] and C is the boundary of the…

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Q: -(1,2,3) What should m be for the integral S00 (2xyz? + 3)dx + (mx²z³ – 2)dy + (3x²yz² + 4z)dz to be…

A: The curl of a conservative field, F→ is 0→ . In that case, the line integral of F→ is path…

Q: 2. Let C be the positively oriented boundary of the square whose sides lie along the lines r =±1 and…

A: According to cauchy’s integral formula for C region:

Q: Evaluate the line integral, where C is the given curve.   z2 dx + x2 dy + y2 dz,   C C is the line…

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Q: if a = 2, b = 6, c= 3 2. Let f(2) = x2 + iy? where x and y are the real and imaginary parts…

A: For the solution of the problem follow the next steps.

Q: a change of uaria bles to evaluate X-24 dA where R.isthe use the integralS, 3x-Y R Parallelogram.…

A: Given integral is ∬Rx-2y3x-ydA where R is the parallelogram enclosed by x-2y=0, x-2y=4, 3x-y=1and…

Q: J Express the interval in (a-R, atR)d 1 x_- alcR and

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Q: I f is analytic and not Canstant in the Prinsple Q-2 interior of a region, then | f(2)l has no…

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Q: Evaluate the integral 9y-x-3x-dz, where Cis the straight line from z = O to z = 1+ i. A 14 B. -14 ©…

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Q: 5. Let R be the region in the first quadrant within the circle z² + y? = 4, outside the circle (z –…

A: Region is in the first quadrant :-    Hence, region the region between these circles in above…

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

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Q: The path integral v- dr, where v = (sin y, x - cos y) and C is the perimeter of the triangle formed…

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Q: Evaluate the integral (xy + xy²) dx + (2x² + x²y) dy over the curve C, defined by going in a…

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Q: Evaluate the integral of F(x,y) = x^2 y^3 in the rectangle with vertices (5,0);(7,0);(7,1);(5,1)…

A: We have to evaluate the integral of F(x, y).

Q: Set up and evaluate an integral that represent the length of the curve. x=r-r', y=p",15 4 3/2 3 4.

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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: Set up, but do not evaluate, an integral for the length of the curve.x = y + y31 ≤ y ≤ 2

A: Formula:

Q: 7. Evaluate the line integral, fe(r +y?)dr+(4z+y)dy, where C is the straight line segment from (6,3)…

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Q: Z[V-1] is a principal integral domain O True False acer

A: This the question of Ring theory .

Q: Express the solution of the follawing IVP in terms of the convolution integral: y" + 4y' + Hygt)…

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Q: Evaluate the integral by making an appropriate change of variables.   7(x + y) ex2 − y2 dA,…

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Q: Set up, but do not evaluate, an integral for the length of the curve. y = x - 3 In(x), 1< x < 4 4 dx

A: The given curve y=x-3 ln(x), 1≤x≤4

Q: 2. Let C be the positively oriented boundary of the square whose sides lie along the lines r ±1 and…

A: According to cauchy’s integral formula for any region C,

Q: the hat cquetin to solve t yo and. use seperation. method of Variables on boundary data : ult,o] =…

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

A: the line integral f F dr, where F = [ry, yz, xz] and C is the boundary of the hemisphere x² + y² +…

Q: 川- Q1 Verify that [(y² – 2x )dx +(2xy +x² )dy = [[] dA where C is the boundary of a regi ôy R R…

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Q: 2 (2y-y² 15. Evaluate the integral / x² + y²dzdydx by using cylindirical coordinates.

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Q: 4. Find all local extremum of the functionf (x,y) = x2 – y2 bounded by the circle x2 + y2 = 1: %3D

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Q: 3. Find the extreme values of the given f(x, y) on the indicated surface. f (x, y) = 8x² – 2y; x² +…

A: The solution of the problem is given in the next step.

Q: Set up, but do not evaluate, an integral for the length of the curve.x = y + y45 ≤ y ≤ 6

A: Here we are given x in terms of y and limits on ySo we use this formula of curve length.

Q: 2. Find the value of the integral of g(z) around the circle |z- il = 2 in the positive sense when 1…

A: Cauchy integral formulae: Let us define function f: D→ℂ and a∈D and 'C' is any closed curve around…

Q: f(x, y) - x/y over the region in the first quad- rant bounded by the lines y = x, y = 2x, x = 1, x =…

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Q: 4. Find the area enclosed by: a. y= sin(x) and y cos(x), x=0, x = and the y-axis. b. y=x and y =Vx.…

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Q: ASK YOU Evaluate the given integral by making an appropriate change of variables. 6. x - 8y dA,…

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Q: 2) Let C denote the positively oriented boundary of the square whose sides lie along the lines x =…

A: Given line x=-2,2 &amp;y=-2,2 is can be  solve as follow

Q: By making an appropriate change of variables, evaluate the double integral (x + y)e²"-v° drdy where…

A: Suppose that we want to integrate f(x,y) over the region R. Under the transformation the region…

Q: Let f (z) = x² + iywhere æ and y are the real and imaginary parts, respectively of z and C is a…

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Q: Evaluate the triple integral: A 24 B 6 12 18 √₁³√₁² √²(x + y + (x+y+z)dydxdz

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Q: 4) Using Green's theorem, convert the line integral f(6y² dx + 2xdy) to a double integral, where C…

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Q: The area under the curve y = 3z bounded by the linesI = 3 and z= 7 above the z- azis is O 174.00…

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Q: Evaluate the double integral (x+ y)dA where y = | x| and the line y=4 16/3 O 32/3 O 128/3 O 64/3

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.