Assume a to be a nonzero real no.. Determine the area of the portion of surface xy = az in the fir octant which lies inside the cylinder x² + y? = a?

Q: Determine the area enclosed by the following curves r = 2 + cos 0 97/2 r = 4 + 3 sin 0 7/12 + v3/16

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Q: Use Green's Theorem to evaluate the integral o (3x - y)dx + 4xdy where C is the circle x +y? = 1…

A: Consider the given integral. ∮C3x2-ydx+4xdy Here C is the circle x2+y2=1 The Green's theorem can be…

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

A: Jacobian of the transformation x=g(u,v) and y=h(u,v) is  ∂(x,y)∂(u,v)=∂x∂u∂x∂v∂y∂u∂y∂v Suppose that…

Q: Find the surface area of the sphere with radius of 7 in. Leave your answer in terms of T. 287 in 2…

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Q: By using polar coordinate, evaluate Sl, x² + y² dA, if R is the region in between circle x² + y² = 1…

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Q: Find the area of the surface S where S is the cap cut from the paraboloid z = 2– x – y by the cone z…

A: Given that : z=2-x2-y2z=x2+y2 Now, to find the point of intersection , 2-x2-y2=x2+y2Put…

Q: Consider the surface S: z = 4 - x2 ,bounded by y = −5(x2 - 1) and y = 0, just as it is shown in the…

A: We have to find the area of the surface S, and we will use surface integral to do that.

Q: Evaluate yds where S is the surface = x + 2y?, 0 <a < 1, 0<y S 2

A: Consider the surface, z = x + 2y²

Q: In RST, U is the Centroid. If SQ=6, find SU and UQ W R

A: Given query is to find SQ and UQ.

Q: 6. Use Green's Theorem to show that the area of the unit disk x2 + y? <1 in R? is T by evaluating a…

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Q: What is the value of the closed integral cos(iTiz)/z with respect to z within the closed circle /z/…

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Q: Which one of the following surfaces is the aph of f(z, y) = y -2 ? 3..

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Q: Set up, but do not evaluate, an integral for the length of the curve. y = xe, osxS 8 dx Jo

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Q: Use Green's Theorem to evaluate . ydx – xdy where C is the cirde centered at the origin

A: Given integral ∮Cydx−xdy, where C is the circle centered at the origin with radius 4 We have to find…

Q: Calculate the area of the surface S. x2 that lies between z = 2 and z 6. S is the portion of the…

A: A coordinate system is a convention that is used to represent a point uniquely using a set of…

Q: 2. Fnd the area of the sur face in the first octant cut from the cone z2 = x2 y2 by the plane x +y =…

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Q: Find the surface area of a sphere with radius, r=8 in. S.A. = in (Type an exact answer in terms of…

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Q: Use Green's Theorem to evaluate the integral (x² - y)dax + 3xdy where C is the circle x² + y² = 1…

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Q: The area of the surface p = 2, 0sz<5,0<¢< T is 201 Select one: O True O False

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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: / y cos(r*)dA. R

A: Given:- Let R be the region in R2 bounded by the x-axis, the parabola y = x2 and the line x = 2

Q: Evaluate the integral į. I. (1 - x - x² – y²)dA Where R is one-unit circle on the xy-plane.

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Use geometry to evaluate ∫∫∫R 1 dV where R is the region inside the sphere x2+y2+z2=4.

A: Given R as the region inside the sphere

Q: Find the surface area of the portion of the surface z = xy which is inside the cylinder p2 +3? = 9.

A: It is given that the portion of the surface is z=xy=fx,y. The surface area of the surface is…

Q: Evaluate the integral /R 2xy dA, where R is the triangle 4x + y 0, y 2 0.

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

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Q: By changing the independent variables z and y to u and r by means of the relations u=z-ay, v=z+ay,…

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Q: Use the surface area formula SA = /I. V1 + f% + f; dA to prove that the surface area of the sphere…

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Q: Use Green's Theorem to evaluate the integral (x² – y)dx + 4.xdy where C is the circle x? + y? = 25…

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Q: Consider the inetgral (11z + 2) dA where Ris the region between the circles z? + y? = 9 and z2 + y?…

A: Since R is the region between the circles x2+y2=9 and x2+y2=100. Therefore, we describes the region…

Q: O (x² – y²) dx + x dy where is the circle x + y² = 9.

A: Green's theorem states that ∮CM dx+N dy=∬R∂M∂y-∂M∂ydx dy Here M=x2-y2 and N=x Hence the integral…

Q: SSx x dA; R is the portion of the disk x +y s 16 in the second quadrart

A: According to the given information, it is required to find the value of the given integral.

Q: Find the value(s) of c such that the area of the region bounded by the parabolae y = x² – c² and y =…

A: Topic = Application of integration

Q: Find the areas of the regions Inside the cardioid r = a(1 + cos θ), a &gt; 0

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Q: Prove that dr-V3Ta? where こis the intersection of the plates: x²+ and and F=ly,Z,x)

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Q: Find the value(s) of c such that the area of the region bounded by the parabolae y = x² – c² and y =…

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Q: Find c > 0 such that the area of the region enclosed by the parabolas y = a? – c² and y = c – a? is…

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Q: Use Cauchy's Integral formula to evaluate the integral: Sa (z+1) e2z dz where C is a circle |z| = 3.…

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Q: c). For each of the given paths, verify Green's Theorem by showing that [y³dx + xºdy=ff(xXx dA.…

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Q: Consider the surface: S:z = 4 – a?, in the first octant and bounded by x² +y°, as shown in the…

A: The equation of the surface given is as follows: z=4-x2 The surface is bounded by the curve x2+y2=4.…

Q: Evaluate ffp(4xy + 1) dA, where R is the region in the upper half-plane bounded by the circles a? +…

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Q: (3z+1) z'e (b) $1+2 z'e² (a) p- - dz -dz 3 (s + z7)(1– z)z?

A: Evaluate the given two integrals over the circle z=4 (a) Let fz=3z+12zz-12z+5 The singularities of…

Q: let s is the curved surface of the cylinder x²÷a² + y²÷b²=1 0≤z≤c , then evaluate…

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Q: B9. (a) Use the Cauchy integral formula to find zdz (z + 1)(22² + 3z –- 2) | where I is the circle…

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Q: Let S be a simple closed positively oriented contour whose graph is shown below. Using Cauchy…

A: Note "As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly…

Q: Given that o is the part of the surface z = 4 – x in

A: Given, the surface z = 4 - x in the first octant from y = 0  to  y = 2. If ψx, y, z=xyz, F(x, y, z)…

Q: Find c > 0 such that the area of the region enclosed by the parabolas y = 390. c and y = c² – a? is…

A: we know that areaA of the region enclosed by given parabola is given by A=2∫-ccc2-x2dx=4∫0cc2-x2dx…

Q: Evaluate || 4.nds , where A=zi+xj – 3y°zk and S is the surface of the cylinder x² + y =4 included in…

A: Let ∅=x2+y2-4  Then the normal to the surface S is ∇∅=2xi+2yj The unit normal is…

Q: By changing to polar coordinates, evaluate the integral where D is the disk x² + y² ≤ 25. [][₂₁x² +…

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