2+ y² = 4 r = 4- cos (0) Caroioter the imtegral I= | R1 R2 R in XY plane given by R=Ri URz 4 when trenstormng the integmal to ! you get? pohr coordinatasl

Q: A curve C is the boundary of a shaded region D which defined by y = 2x-4 and y = 2x in…

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Q: Let F = (x,y) and C be the circle of radius 5 centered at the origin oriented counterclockwise.…

A: Let F=x,y and C be the circle of radius 5 centered at origin oriented counterclockwise. We have to…

Q: 8.Evaluate the triple Integral. Te by The paraboloid X=2yt + 2z? and the plane X=2. 7x dV, where E…

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Q: 1) Find the vdlemes of the oolids generated by revolving the resion in the first quuadrant bounded…

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Q: (a) Evaluate ([ Á.ds where A=(x+y²)î-2xj+2yzk and s is the surface of the plane in the first octant…

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

Q: 1. Under the paraboloid = 3z2 + y? and above the region bounded by y = x and r= y² – y

A: Find point of intersection of:  y=xx=y2-y y=y2-yy2-2y=0y=0,2

Q: Evaluate the line integral y = x² from (-1, 1) to (1, 1) and the line segment from (1, 1) to (−1,…

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Q: The plane figure below is a square of side length 2 with a quarter circle of radius 1 taken out of…

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Q: 52. Show that a spherical cap of height h and radius R (Figure 19) has surface area 2n Rh. Rogawski…

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Q: Find the area Inside the cardioid r=2 cos (6/3) and outside the circle of radius r = vZ centered at…

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Q: Find the area of the part of the eircle r-4 sin that lies within the sector 0 50s 87 -2/3 3 + V3 3.…

A: It is given that,r=4sinθ, that lies within the sector 0≤θ≤π3we have to find the area of the part of…

Q: Find the potential u(x, y) for u +u =0 in the rectangle 0<x< 2 and 0 < y s 2, if the upper side is…

A: The given problem is to solve the potential u(x,y) Laplace partial differential equation, we have to…

Q: Po Prove that fcz) = zis coutinuous at z=z. O Prove that. fZキ2。 is dis continnity at z=Zo, where Zn

A: (1) we have to prove that                                                              f(z)=z2 is…

Q: roblem 12. Calculate the volume under the elliptic parabolold z 4z + 8y and over the rectangle R…

A: The given region is z=4x2+8y2 and over the rectangle R=-4,4×-1,1. We have to find the volume under…

Q: 1. Evaluate the line integral -ds y+z where C is the curve r= y², y + z = 4 from (4. 2, 2) to (0,0,…

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Q: 2. Use Green's theorem in order to compute the line integral P (x – 4)³ dy – y³ dx where is the…

A: We need to compute the given integral using Green's theorem . ∮C(x-4)3dy-y3dx Where is the circle of…

Q: integral Over the é dz Z-2 the Compute %3D Curve C below lm (2) Relz)

A: In the given question we have to find the value of the integral I over the curve C. and the given…

Q: 2). Find the flux of F(x, y, z) = (0, yz, z) outward through the surface S cut from the cylinder y +…

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Q: Jse Green's theorem to evaluate the ne integral (2tan x _cos 2y³) dx + (7⁰s y + 2x (πº where is the…

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Q: 2. Evaluate directly the line integral fo a dy where C is the quarter-circle from (0, 4) to (4, 0)…

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Q: İki noktalı Gauss kareleme yöntemini kullanarak S dx integraline 1+16x4 yaklaşık değer bulunuz. 2…

A: we have given by integral ∫-12128x21+16x4dx we have to solve the integral by using two-point…

Q: Evaluate the line integral (direct method) | (3x– y) dx – x dy , where C consist of the parabola…

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Q: D Use cylinedrical coordinates to calca late the integral f fex,y,2)=2 above thedisk *ry?s4 in and…

A: given  disk x2+y2≤4 surface z=16+x2+y2 to find  to calculate the integral of fx,y,z=z over the…

Q: Q3// A surface S is defined by 2x2 + z 1 and the bounded by the planes y = 0,y 2, x = 0,z = 0 in the…

A: A surface S is defined by 2x2+z=1 which is bounded by the planes y=0, y=2, x=0, z=0 in the first…

Q: 1. The solid bounded by the cylinder y = 9 – x² and the paraboloid y = 2x? + 3z².

A: In this question, we find the volume bounded by given surfaces. The surfaces: y=9-x2andy=2x2+3y2 The…

Q: 48.) Find work done by F (2x³y* + x, 2x*y³ + y) along the path r(t) = (t cos(nt) – 1, sin (t)) 0sts1…

A: We have to set up parameterization form in line integral in part (a)  And We have to prove that F is…

Q: 8. Verify Green's Theorem for + (6y – 3y +z) dz + yx°dy where C is shown below by (a) computing the…

A: Let F=Px,yi+Qx,yj be the vector field and C be the boundary of the region D. The Green's theorem…

Q: 3. The solid bounded by z = 0, z = 1 – x², z = y and 2y + z = 12.

A: Given that  Region z=0,z=1-x^2 and 2y+z=12  To form a triple integral

Q: 15.) The solid in the first octant bounded by the coordinate planes and the plane 3x + 6y + 4z = 12.…

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Q: Evaluate the line integral (direct method) |(3x– y) dx – x dy , where C consist of the parabola y=…

A: Given integral is, ∫C(3x-y)dx-xdy

Q: Use Green's theorem in order to compute the line integral (2sin z + 3y²) dx + (sin(4®) + 2x³) dy…

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Q: Find a parametrization of the curve. The intersection of the surfaces z = x^2 − y^2 and z = x^2 + xy…

A: Given : The surfaces z = x2 - y2 and z = x2 + xy - 1.   To find the parameterization of the curve.

Q: How do I set up the triple integral of the function xy2 -3z, where the solid is bounded by the…

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Q: 7. Find the flux of F(x, y, z) = x î+ y ĵ+ z² k across the sphere of radius 1 centered at the origin…

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Q: 8) Find the moment of inertia about the x-axis of a thin plate bounded by the parabola x = y - y?…

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Q: 2/ Find the line integrals of the ellipse+3= ellipse by x = acos(t) ,y= bsin(t) 1 , parameterize the…

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Q: 8.) Find work done by F = (2x³y* + x, 2x*y³ + y) along the path r(t) = (t cos(at) – 1, sin (t))…

A: Since we have given that F = 2 x3 y4 +x, 2 x4 y3 +y   and rt=t cosπt-1, sinπ2t    drt = cosπt -t…

Q: Use spherical coordinates to evaluate the integral •√₁-x² √√₁-x²-x² (x² + y² + ²)dzdydx.

A: To evaluate the integral using spherical co-ordinate system :-

Q: Oue Sol ue have Surface ズ= 4パーナ at (-11214) DHerentiak partially fimidız) with r to 12 Sx= 811 Nou…

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Q: 4| ind Volumes of のnen reo リュー! )ス"0) reten iegTon 1- dv - dzdy chy 1 Limik of 2:0> y2 Limik of y:…

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Q: Calculate the line integral f(-102 + 4z + 5) de + (-7z – Oy? – by – 4) dy, where Dis the annulus…

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Q: No. Date Evaluate fff dv G x² + y² where G is a solid that lies inside cylinder *+(4-2)² =4 obove…

A: we will use cylindrical co ordinate system to solve the given integral

Q: Evaluate the circulation of Gayi + zj+5yk around a square of side 9, centered at the origin, lying…

A: Solution :

Q: Answer the following question. The wake velocity of the lift Oseenlet is given by 1 w" = 2 rpU x,…

A: The velocity of lift Oseenlet is wi=12πρUcij3∂∂xjekx1K0kr (1) The horizontal component of velocity…

Q: Find the line integral of z2 dx + y dy + 4y dz, where C consists of two parts, C, and C,. C, is the…

A: Given line integral ∫Cz2dx+ydy+4ydz, where C consists of two parts C1 and C2. C1 is the intersection…

Q: Use Green's Theorem to evaluate the line integral , 6y² dx + 5x² dy, where Cis the boundary of the…

A: Green's Theorem: ∮C(Pdx+Qdy)=∫∫R∂Q∂x-∂P∂ydA

Q: 3. Set up the formulation to find the surface generated when the curve y = x² is revolved about the…

A: 1st we need to convert the curve in x=f(y) form and corresponding limits for y , Then use given…

Q: 3. Evaluate the triple integral || ryz dV; G is the solid in the first octant that is bounded by the…

A: To evaluate the given integral ∫∫∫Gxyz dV. The limits are given as  z=0 to z=2-x2 and y=0 to y=x and…

Q: 2) Use a change of variables to evaluate , zdV; where Dis bounded by the paraboloid z = 16 – x - 4y?…

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Q: The intersection of the ellipsoid x2 + 4y2 + z2 = 4 with the plane z= 3x gives an ellipse C. A)…

A: Given that the ellipse C is the intersection of the ellipsoid x2+4y2+z2=4 with the plane z=3x.