4. Given the uketch °f graph: su rFace x* + y2.= 9 - z 3 3 a. Find above of the uving polar the sur pace area the Xy plane Coo rdinafee CS

Q: Find the exact arca of the surface obtained by rotating the curve: 3 24 = 5 sin Tr, 0 <I<1 about the…

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Q: known as the loop of Descortes lea ond tor EECO,00) O(t)= ( 3+2 %3D Calculate the oreo of the region…

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Q: Find the area of the surface generated by revolving the curve about each given anis. *- 7t. y= st,…

A: We have to find  the surface area generation by revolving the curve about x and y axis

Q: a The curvature of the helix r(t) = (a cos t) i + (a sin t) j + bt k (a,bz 0) is K=- What is the…

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Q: Evaluate COS Z -dz , where C is the circle |z – 1| = 3. (Integrate counterclockwise around C.)

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Q: 32. At what points does the helix r(t) = (sin t, cos t, t) intersect the sphere x? + y² + z² = 5?

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Q: The centroid of the half-ellipse-shaped-cross-sectional area shown is given by: 4 Ye 9 - 25m9-y² dy

A: Given half ellipse shaped cross section is:…

Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = Vx, 1sy& 4

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Q: Consider the shaded square region on the s-plane, as shown in Fig. Q1. Let p =-Co, + j@, 1-5?, S'-…

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Q: | (4x – y? + 6z)ds

A: We have to find the line integral of the function : 4x - y2 + 6x Along the curve C , which is the…

Q: T. 9. TO = PO 10.Sector of a circle is the region bounded by two radii and their intercepted arc.

A: here we check whether the given statement is true or false.

Q: If C is a circle of radius 8 centered at the point ( 0, 5 ), then evaluate pain(2dr + (11æ sin(y*…

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Q: 9) Find the area of the surface generated by rotating about the y-axis y = x' between (0,0) and…

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Q: .If C is the circle (traversed once counterclockwise) of radius 2 with center at z = 0, %3D 7e?…

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Q: Find polar equaton or the curve represented by the given Cartesian equaton 5at +j=8x(ris not equal…

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Q: A Cartesian equation for the parametric curve x=24sin?e, y=21cos20, n ses 31/2 is given by O…

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Q: The area of a cylinder sector with radius r and central angle of radian measure 0 is A = r20, and…

A: If the area of the sector is 1 sq. unit, then A=112r2θ=1θ=2r2          ...(1)

Q: 4. Consider the surface S parametrized by R(u, v) = (uv, sin u, cos v). Find an equation for %3D the…

A: The given curve S is parametrized by: R→(u,v)=uv,sin u,cos v Now, to find the equation of the…

Q: 4. Let C denote the circle |z – 2i| = 1, taken in the usual counterclockwise orientation. Compute by…

A: Given: Let C  denote the circle z-2i=1 z-2i=1x+iy-2i=1x+iy-2=1 So, Centre of circle will be 0,2 and…

Q: T 9. TO = PO nrre CHOICE 10.Sector of a circle is the region bounded by two radii and their…

A: We have to identify true or false.

Q: Let C be the spiral para me terized by t/10 cos (t) P + e sin Suppose y ou shartrom (e, o) and…

A: We have to find the position after travelling 10 units.

Q: The unit circle x² + y=1 can be wrriten in parametric form as x = cos(0) and y : = sino. dy and…

A: Follow the procedure given below

Q: Figure I below shows a uniform lanmina in the form of right angled triangle OAB with right angle at…

A: 5(ii) Solution: In part (i) centroid of sector OPQ has been calculated as  Ox= 4a3π and Oy= 4a3π…

Q: Consider curve C which is the intersection of the surfaces shown in the attached figure. image 1…

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Q: 4. Given YZ tangent to oJ at point Y and m<WYZ = 104, %3D what is the measure of WXY?

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Q: 13. dy/dx = 2x, У (0) 3D —1

A: Solution: dy/dx =2x  ,    y(0)=-1

Q: Given the cardioid r= 3(1+cosθ) 0 ≤ θ ≤ 2π Determine in wich points the cardiod has vertical…

A: Differentiate the equations r=31+cosθ and x=rcosθ with respect to θ, to find drdθ and dxdθ.…

Q: The shaded band shown here is cut from a sphere of radius R byparallel planes h units apart. Show…

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Q: Consider the region 2 enclosed by the curves I', and I': given by: T: y=1 Ti y=(x- 1)²

A: Given curves are, Γ1:y=1Γ2:y=x-12 So, the required diagram of the given curves are,

Q: The unit circle x² + y = 1 can be wrriten in parametric form as x = cos(0) and y = sin0. dy Find and…

A: The unit circle can be written in parametric form as x=cosθ and y=sinθ We have to find dydx and the…

Q: Show that the surface area obtained when the arc of the parabola y? = 16az from I = 0 to r = h is…

A: Surface area

Q: Find the sope of the tangent ine tothe Given polarcove at thepointspecifiedby the valbe Of e 2.

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Q: Use the formula area(R) = } for T dy – y dæ to find the area of the sector R of the ellipse that is…

A: Consider the provided question, We need to find the area of the ellipse that is swept out by the…

Q: The unit circle a + y: =1 can be wrriten in parametric form as x = cos(0) and y= sin0. Find and…

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Q: 2. The Cornu (or Euler) spiral, shown below, is defined by r(s) = (f* cos (u²) du, f *cos (u²) du,…

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Q: What surface does the curve r(t) = -t cos(t), 121 -t sin(t), t) lie on? 121 1 x² + y? 121 Oz =…

A: First define the curve of the surface r(t) = &lt; x(t), y(t), z(t) &gt;

Q: Page 9 9. The curve y = x2 with 0Sx<1 is rotated about the y-axis. Find the exact area of the…

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Q: 1. Draw the curve r² = 2a? cos 20, a > 0 and calculate the area enclosed by this curv

A: This question is about application of integration in polar coordinates

Q: s) Evaluate the line itegral ( +2y + 2)dy – dz, where C is the arc of parabola z = 2+ y". from (2,0)…

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Q: Find the unit fangent sector t for the currve : r=ti -2tj + 3t°k Y =a sin wt i +a Ceswt j %3D 2- r…

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Q: Find the length of the spiraling polar curve r = 2e60 From 0 to 2T. The length is

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Q: Given polar curves A₁: r = 1 + sin 0 and A₂: r = 3 sin 0 1. Set up (but do not evaluate) an…

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Q: 2. Use Green's theorem to evaluate fe e-x³ dx + (5x + sin(y²)) dy, where C is the circle x² + y² = 4…

A: Please see the below picture for detailed solution.

Q: Sketch the regions enclosed by the given curves y-4 cos(7x), y- 4 sin(14x), x -D, x-/14 0.05 0.10…

A: The solution of above question is written below.

Q: A curve is defined by the parametric equations z (t) = at and y (t) = bt, where a and b are…

A: Given,  We have  xt = at   and yt = bt  ;  where a and b are constants.  We have to find the length…

Q: Use polar coor dina tes to eva lsote the arra of the region bounded above by the unit circle betaw…

A: One of the two main parts of calculus which are concerned with the study of integrals, as opposed to…

Q: Evaluate fe kz ds where k is a constant and is the circular helix with parametric equations T = Cos…

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Q: Find the polar eauation for the curve represented by the given Cartesian eavation. Dy=-4x² 1.

A: We need to find polar equation.

Q: The unit circle x² + y=1 can be wrriten in parametric form as x = cos(0) and y = sin0. dy Find and…

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Q: 3 dz where C, is the top half of circle with radius (b) Compute the upper bound of 2,

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