3r + 4y for all (r, y) eR where R is the 4. Find the area of the plane z = region in the first quadrant which is bounded by the circle r = 8sin (0) and the lemniscate r = V32 cos (20) both given in polar coordinates. Give your 19 of 30 answer to the nearest four decimal places. 2 2 A(S) = || 1+ dA, + ду R where R is the domain over which we are interested to find the area of the surface z. Sketch the region R before doing the integration. (In polar coordinates, dA = rdrd0)

Q: (4) Find the surface area of the cone S a) b) c) d) 7-√√2 5-√3 p(r, 0)=(r cos 0,r sin 0,r) for 0≤0…

A:

Q: x³ +1 Q3: Find the length of y=√x+2,1 ≤ x ≤ 7, Using ds = 1+²dy into the surface area of the object…

A: Find the arc length of y=x+2, 1≤x≤7 using the differential element ds=1+dxdy2dy. For formula for…

Q: 1 2 Use polar coordinates to evaluate the area of the region bounded above by the circle x? + y? –…

A: This question is about application of integration

Q: 5) Let S be a surface composed of the union of the surfaces S1 and S2 with equations S1: 4z + x? =…

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

A:

Q: Consider the curve in the x=0 plane given by the equation z=17/5y^2. Let S be the surface of…

A: To determine the radius of the circle S∩E  we have to find the equation of the intersection-curve…

Q: (1– y°)dx+(x° +e )dy, where C is the boundary of the region between the circles x2 + y2 = 4 and x2 +…

A: Given integral, ∮C1-y3dx+x3+ey2dy Here C is the boundary of the region between the circles x2+y2=4…

Q: 9.3.16. Compute the surface area of the surface obtained by revolving the given curve about the…

A: (a) To compute the surface area of the surface obtained by revolving the given curve about the…

Q: (c) What is the image of the unit circle D = {|z| <1|z€ C} under the Mobius transforma- tion T(z) =…

A:

Q: Let F = (5z + 5x²) i + (7y + 4z+ 4 sin(y² )) J + (5x +4y + 7e²) k. (a) Find curl F. curl F (b) What…

A: We’ll answer the first three subparts of the question since the exact one wasn’t specified. Please…

Q: Evaluate fS (3x + 4y²)dA by changing it into polar coordinates over the region in upper half plane…

A: In polar coordinates

Q: 3. 3) 6) X= y 〇s454 6) Find the area 0f the surface of rotation Created by ocyEd curve about the 3.…

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

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

A:

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

A:

Q: The area of the surface obtained by rotating the curve y = 1<xse about the line x = 32 is ** 12 (32…

A:

Q: 3.4.4 By transforming to polar coordinates, show that the double integral (x² + y²) ² dx dy (xy)²…

A:

Q: (2) Use the transformaiton u = xy, v = x² – y? to find JJ (æ* – y*)e*³ dA where R is the region in…

A: Given: The region bounded by the hyperbola xy=1 &amp;3, x2-y2=3 &amp;4 Where u=xy and v=x2-y2

Q: 1. Find the region in the xy-plane in which the following equation is hyperbolic: [(x-y) -1]u +2uy…

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Q: Let R be the region in the second quadrant of the xy-plane that lies between the circles x? + y? = 5…

A: The concept knowledge of the polar form helps to find the required answer to the problem. In the…

Q: (d) Let 0 arg(z). Take C to be the wavy contour in the z-plane described by 0 < arg(z) < T; |2| =1-…

A:

Q: 17. Evaluate the integral: S, 9x? – 6dx. 18.Determine the center of the circle x² +y² = 25. %3D

A: (17)  Given that I=∫-159x2-6 dx It is known that ∫xndx=xn+1n+1 So, I=9x33-6x-15 =3x3-6x-15 Now we…

Q: 4. Consider the saddle surface r y?- z², find the equation for the tangent plane at the point (0,1,…

A:

Q: B. Evaluate the given line integral. Follow the direction of C as given in the problem statement. 3.…

A: The given integral is ∫C2-xydS where C is the upper half of the circle centered at the origin of…

Q: 3) consider the regionnin the second quadrant betueer the circles x?+yZ=4andx2+y2=25, and above the…

A:

Q: 2. Obtain the eccentricity e and centroid a, and y. of the following image. f(x.y)=1 (object: dark)…

A: From the figure, we have to write down all the dark box function, for which f(x,y)=1 x,y=3,2, 4,2,…

Q: Given: f(x,y)=x-2y+3 and D is inside x +y =16 and to the right of the y-axis. Write the integral K =…

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Q: Find the surface area of the part of the surface z = x2 + 3y that lies above the triangular region T…

A:

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: 135 2. y = x³, y = x + 6, and 2y + 2 = 0 (Answer: s. u.) 4

A:

Q: z + 29; The value of integral (cosx,5z",6z+z sin x)·(x,y,z) ds where s is the surface of sphere x² +…

A: Please find attachment for the details solution

Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = -x2 -…

A:

Q: T Find the area of the plane region. 0≤x≤ bdunded by y=sin x. x = 2 2 1.111 s.u. π²-4 S.U. 1 s.u. EN…

A: We can solve this using given information

Q: E Find The onea z the su face, uoing Polar Coordinaks, of the porton of tho cone bre rg-a2=0 between…

A: Surface area of a surface z=f(x,y)  A=∫∫D1+fx2+fy2dAD is the region on xy plane

Q: (b) Find the area of the surface obtained by rotating the region bounded by the curves 7 35xy 5y12+…

A: To find the area of the surface obtained by rotating the region bounded by the below curves about…

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

A:

Q: 7 sin(æ), æ = T, I = 27 and The region R in the first quadrant of the xy-plane is bounded by the…

A:

Q: S y = 3 – 2 4z – 4 = 3(x +1)?

A: Let us start solving the problem step by step

Q: 4. Find the value of the integral 223 + 5 'zp- c (z – 1)(2² + 9)* taken counterclockwise around the…

A: The objective is to find the value of the integral ∫C2z3+5z-1z2+9dz

Q: EVALUATE § 7. d² USING STOKE'S THEOREM 3xz^ + ex² ₁ + 2xy^ с F(x, y, z) = 3XZ1 te C IS THE CIRCLE…

A:

Q: Use polar coordinates to describe the region shown. y 10 5 -10 -5 10 5 -10 R = {(r, 8): 0 srs 3…

A: Here we will use some points and shape of given graph to decide which equation representing it .

Q: 3z2+z+1 Q4. (a) Evaluate using Cauchy's integral formula Sc (z2–1)(z+3) dz where C is the circle |z|…

A: The given problem is to evaluate the given complex integral over the given region using cauchy…

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

A: Consider the equation of the plane, z=4x+y for all x,y∈R,where R is the region in first quadrant…

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: Determine which of the following gives the area of the surface obtained by revolving the curve y =…

A: This question is related to surface area. We will solve this question by using formula of surface…

Q: Find the area of the surface generated when the curve y=1/4(e2x + e−2x)is rotated about the x-axis…

A:

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

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Q: 33. Find the surface area of the portion of the curve x²+y²4 from x₁=0 to x-2 when it is revolved…

A: We need to determine the surface area that is resulted when the portion of the curve: x2+y2=4 from…

Q: Q#4 a. Find the area of the surface generated by revolving abuut the x – uxis the portion of the…

A:

Q: ez C z(2z+1)² Evaluate the integral S dz where C is the unit circle with counterclockwise…

A: Here given ∫Cfzdz=∫z=1ezz2z+12dz Thus fz=ezz2z+12 or fz=ez4zz+122

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.