(c) Evaluate dx dy 1– x² – y² where R is the right half-disk of radius % and centered at (0, % ).

Q: Evaluate the line integral y dx +xdy; C is the curve x = 4t, y = t³ – 1, 0sts 1. Jy dx + x*dy (Туре…

A: Consider the provided question,

Q: 1. Find Sp(r+2y)dA, where D is the region bounded by the parabolas y = r2, and y=1+2

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: sin y dV, where E lies below the plane z = x and above the triangular region with vertices (0, 0,…

A: Given, the region E lies below the plane z = x and above the triangular region with vertices 0,0,0,…

Q: The area of the surface generated by revolving the curve y=x² if 0<x<2 about the y-axis is given by…

A:

Q: Evaluate the line integral. y dx - x dy, parabola y = x² for 0 < x < 8

A: Given:

Q: 18. Show that the centroid of the sector in Figure 13 has y-coordinate 2R sin o (0, y) R FIGURE 13

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Q: Determine the exact area between the x-axis and the curve defined parametrically by ¤(t) = ;t2 1…

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Q: y2 %3D 1. 60. x²y dx dy dz, T: Region bounded by 4

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Q: Find the parametrization of the tangent line to the space curve r(t) = (e" , sin(t), (t + 1)-³) at t…

A: Given that  r(t)=(e^(4t),sin(t),(t+1)^(-3)) at t=0 We have to find out the parameterization of the…

Q: Evaluate dx dy x² – y? where Ris the right half-disk of radius ½ and centered at (0, ½ ).

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Q: Find the surface area of the curve: y In x; 1sx S 2 when the curve is rotated about the y-axis.

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Q: JJ xy²z dv where D is the tetrahedron in the first octant bounded by the coordinate planes and the…

A:

Q: 1. Find by integration the area of the surface of revolution generated by revolving the loop about…

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Q: Find dy/dx and d²y/dx² at t = 2 for the parametric curve x = ½t², y = ⅓t ³.

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Q: b. Evaluate the line integral ycos(xy)dx +(xcos(xy)+x)dy where R is the circle x'+y =9 traversed…

A: Solution Given b). ∫y cos(xy)dx+(xcos(xy)+x3) dyevaluate the line integral

Q: =t°, y = t² 3. Set up an integral to find the surface area generated when the given curve x = where…

A: Given:      x=t3, y=t2 Interval 0≤t≤1   Surface area generated about x-axis is…

Q: Give the integral representing the length of the parametric curve x=t^3, y=t^4, 0≤t≤1.

A: Given: A parametric curve:   Now the length of the parametric curve is given by the formula:

Q: Evaluate ∫c (y+sin x) dx + (z2 + cos y ) dy +x3 dz where C is the curve r(t) = (sin t, cos t, sin…

A: ∫C y+sin x dx + z2 + cos y dy + x3 dz = ∫C y+sin x i + z2 + cos y j + x3 k (dx i + dy j + dz k)…

Q: Q4:B/ Find the area of the surface generated by rotating the curve y = e", 0 < x<1, about the…

A:

Q: Evaluate SS x² y4 dx dy D 1 where D is the region bounded by the hyperbolas xy-2, xyalk parabolas y²…

A: We have to Evaluate the integral  ∬Dx2y-4dxdy where D is the region bounded by the hyperbolas xy=2,…

Q: Evaluate the line integral I of the one-form w = xy dx + 12y dy over the parametric curve a : [0,…

A: Given: ω=xydx+12ydy To find: I=∫αω  where α:[0,ln2]→ℝ2 with α(t)=(e2t,e-2t) ∴x=e2t,y=e-2t Now,…

Q: Evaluate the line integral (xy dx + y dy), where C is the curve y = sin(x), 0 ≤ x ≤ π/2

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Q: The area of the surface obtained by rotating the curve y = 1 I+ X, 1 <xse about the line x = 28 is…

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Q: Compute dy/dx and d^2y/dx^2 for the following parametric functions

A: Given: y=e2tsin2tx=e2tcos2t

Q: valuate the line integral Scy da +a dy where C is the parameterized path a = t2, y = t°, 1<t<4. Scy…

A: We have to find the given integral.

Q: Evaluate the integral |xy dx – z dy + 8z dz where C is the curve with parametric equations x = 2t, y…

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Q: Which of the following is the surface area of the surface generated by revolving the curve y = 폴 in…

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Q: Evaluate the line integral (2x + 6)dx + (5y+ x)dy along the curve C: C F(t) = tỉ + 2tj, 0<t<1.

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Q: Evaluate the line integral ∫Cx2ds, where C is a the curve given by the equation y=f(x)=lnx, 1≤x≤e.

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Q: y = logt, x = t -4 %3D

A: Let the given function be, y=logtx=t-4 Put x+4 for t in the function implies, y=log(x+4)

Q: Q7. Use Green's theorem to evaluate fy² dx + 3xy dy, where c is the boundary of the semi annular…

A:

Q: - Evaluate the integral 4-z²-y² 1 dz dy dx Jo 4-z²-y² x² + y² + 2² using spherical coordinates.

A: To evaluate ∫-22∫04-x2∫-4-x2-y24-x2-y2 1x2+y2+z2 dzdydx

Q: Evaluate the line integral 2xyz dx + x²z dy + x?y dz where C is an oriented simple curve connecting…

A: Given line integral is,

Q: Find the area of the surface generated by e +e -y eY + e -y in the X= revolving the curve x= -In 3…

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Q: Find the area of the Surface generated by revolving the given curve about the - axis while x is over…

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Q: e the line integral Sc(3x?y+2)dx+ (x+3)dy where C is the curve r(t) = (t2, 3+t²) with 0 <t < 1.

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Q: 1. Find the area of the surface generated by revolving the given curve about the x-a (a) y = 7x,…

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Q: dy in terms of t: Differentiate parametrically to find dx 1 y = +2 t+1

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Q: Evaluate |(2y+cos x)dx + (5x+ sin y)dy along the positively oriented curve C. C is the boundary of…

A: We have to evaluate the integral ∫2y+cosxdx+5x+sinydy along the positively oriented curve C. Where C…

Q: H.W 1. Find the centre of mass of a thin plate of density & = 3 bounded by the lines x 0, y = x, and…

A:

Q: Evaluate the line integral: [ y dx + x dy ; C is the curve x 1 = t² - 1, y = 6t, 0 < t s 1

A: Note: - Since you have asked multiple questions, we will solve the first question for you. If you…

Q: x² and t %3D 2) = z where E is the region bounded by the parabolic cylinder y

A: We have to set up the integral according to the given information

Q: Evaluate the line integral. y dx + z dy + x dz, r(t) = (2 + t-1, t³, t2) for 0 <ts 3

A: Given: From the above function, the following can be written,

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: Find [R Y · sin xy dA over the rectangular region R = [0, 2] × | 0, .

A: Find the integral         ∫R∫y sin(xy) dA where R is the rectangular region [0,2]×0,π2.

Q: y? cos(22) dz da dy Jy/4 by changing the order of integration to dx dy dz.

A:

Q: 3) Find the area of the surface that results from rotating the curve Y = sin X, 0<X< 1 about the X…

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Q: How many points are there on the surface z = dx +y such that the tangent plane to the surface is…

A: Given :  d=maxa,b,c⇒d=max2,1,0⇒d=2 So,z=dx2+y2⇒z=2x2+y2 Also, dx+y+z=0⇒2x+y+z=0 Let fx,…

Q: sin y 11- nY dA where D is the region bounded by the curve y = vx and the line y=x, if y # 0

A: try not to ask multiple question at a time. solve double integral