Assume the equation for an ellipse is Ax +2Bxy + Cy D where D has the units of area. Show, by performing the proper two dimensional integral, that the area of the cllipse is VẠC – VAC- B

Q: Graph the curve 8y2 = x2 (1 − x2 ). Use a computer algebra system to find the surface area of the…

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Q: Find the area of the surface pf revolution geneeated by revolvinh about y= -2 the arc of the…

A: Given, So, x=y212=gy ⇒g'y=y6 limit of y is from 0 to 6 The formula for finding the area is,…

Q: Find the surface area of the torus obtained by rotating the circlex 2 + (y - b )2 = r 2 about the…

A: Given the equation of the circle  x2+(y-b)2=r2. We need to find the surface area of the torus…

Q: Find the area of the resulting surface if an arc of a parabola y = x? from (1,1) to (2,4) is rotated…

A: Given curve is y=x2

Q: Use the paramteric eauations of an ellipse, x=acos(theta), y=bsin(theta), 0<=theta<=2*pi, to find…

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Q: Which of the following is not a parametrization of the parabola y = r² ? Oz= Vt, y=t Oz-t, y-t Oz- ,…

A: We will check which parametrisation is correct.

Q: Use the parametric equations of an ellipse, x = a cos 0, y = b sin 0, 0 < 0 < 2m, to find the area…

A: Given Parametric Equation of ellipse  x=acosθ and y=bsinθ ,0≤θ≤2π To find the area of the Ellipse

Q: Use the parametric equations of an ellipse, x=4cos(theta), y=3sin(theta), 0 less than or equal to…

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Q: A cube with a cylinder cut from its center is cut along the plane shown. Which of the following is…

A: In this figure cube is just coated outside the cylinder

Q: What is the area of the conic (x + 3) + y 25

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Q: Determine the surface area generated by revolving the line segments about y-axis. 3m 4m 2m 1m 2m 2m…

A: Given , Line segment revolve around y-axis , we have to find surface area of formed shape .

Q: A reflecting telescope contains a mirror shaped like a paraboloid of revolution.If the mirror is 4…

A: When we draw the parabola  to form the mirror on a rectangular coordinate system  we find…

Q: Find the area of the surface generated by revolving the curve, x = /6y – y? ; 2sys 5

A: We’ll answer the first part of this question since due to complexity. Please submit the question…

Q: || 9x2 dA, where R is the region bounded by the ellipse 9x2 + 25y2 = 225; x = 5u, y = 3v

A: Here we use transformation to solve this problem.

Q: Use Green's theorem to find the area between ellipse 16 = 1 and circle x2 + y2 = 25.

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Q: Find the area of the region enclosed by the parametric equation x = t³ - 7t y = 6t²

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Q: (c) . sin (92? +4y?) dA D where D is the region in the first quadrant bounded by the ellipse 9a?…

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Q: use the mthod of trig substitution to prove the area of the ellipse " {(x^2)/(a^2)}+{(y^2)/(b^2)} =…

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Q: Sketch the portion of the surface that lies in the first octant: y= z.

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Q: Use the parametric equations of an ellipse x = 10 cos 0 y = 22 sin 0 0 ≤ 0≤2T to find the area that…

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Q: - Find the area of the ellipse which is parametrically expressed as =a cos o and y=b sin ø, and…

A: To find the area of the ellipse which is parametrically expressed by the below equations.…

Q: What is the definition of a parabolic cylinder?

A: The parabolic cylinder functions are the solutions to the differential equation d2ydx2 + ax2 + bx +…

Q: A hole is drilled through the center of a sphere x?+y² + z² = R,?, leaving a ring-shape solid. If…

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Q: Use the parametric equations of an ellipse, x = a cos(0), y = b sin(0), 0 s 0 s 2T, to find the area…

A: Given: Use the parametric equations of an ellipse, x = a cos θ, y = b sin θ, 0 ≤ θ ≤ 2π,  to find…

Q: Find the area of the surface obtained by rotating the parabola 1 0 <x < 2, about the y-axis.

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Q: find the surfase area of ellipsoid obtained by yevoiving the upper-half of the ellipse…

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Q: Use the parametric equations of an ellipse, D=5 cos(@), y - 4 sin(6), 0 O 27, to find the area that…

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Q: Find the area enclosed by the ellipse x2/a2 + y2/ b2 = 1 shown in the figure.

A: Consider the following equation of ellipse: x2a2+y2b2=1y2b2=1-x2a2yb=a2-x2a2y=baa2-x2

Q: (d) Find the area of the surface generated by revolving the curve y = 2a, 0 < x < 3, about the…

A: Part (D) To find the area of the surface generated by revolving the curve, y=2x,0≤x≤3, about the…

Q: Find the mass of a thin plate occupying the smaller region cut from the ellipse x2 + 4y2 = 12 by the…

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Q: Find the surface area of the portion of the cone 22 = 4x² + 4y? nat is above the region in the first…

A: Given: The portion of the cone is Z2=4x2+4y2 which is bounded by the line y=x and the parabola y=x2

Q: Name the quadric surface: 2x-y²-z²=0 O Ellipsoid O Hyperboloid of one sheet фоалт 340095 t f quant

A: given quadratic equation 2x-y2-z2=0 claim- name the quadratic equation

Q: Find the area of the region enclosed by the parametric equation x = t3 – 8t y = 6t2

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Q: Use the change of variables formula to prove that the volume of the ellipsoid given by ()* + (#)* +…

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

Q: Use Green's theorem to compute the area inside the ellipse x2/32 +y2 /192=1. That is use the fact…

A: Given: The equation of the ellipse is x232+y2192=1. To find: The area inside the ellipse using…

Q: Compute the surface area of the surface generated by revolving one arch of the cycloid…

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Q: The curre y=J36 - z' , -4£ x s4 will be rotated about the ルーaXis. find the area that results af the…

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Q: A hole is drilled through the center of a sphere x2 + y? +z? = R², leaving a ring-shape solid. If…

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Q: An integral expression for the area of the surface generated by rotating the line segment joining…

A: Given that: Points are- (3,1) , (6, 2)

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: Use the parametric equations of an ellipse, x = a cos(e), y = b sin(e), 0 se s 27, to find the area…

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Q: The perimeter of an ellipse is given by P = 4a V1-k-sin-8 de where, k = Using the Simpson's rule,…

A: The given equation of the ellipse is: x242+y272=1 Result: The standard form of the ellipse is:…

Q: I am having trouble solving this.

A: To find the area of the overlap between the interior of the ellipses given below.

Q: 4. Find the area of ​​the surface of the revolution formed by rotating the part of the 4x^2 + y^2= 4…

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Q: Find the surface area of the ellipsoid obtained by rotating the ellipse (=) = 1 about the x-axis.

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Q: Find the area of the region enclosed by the parametric equation x = t³ - 8t y = 4t²

A: This is a loop formed find graph  And then find limits of t

Q: Find the area of the surface generated by removing about the x-axis the upper half of the ellipse…

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Q: Find the exact area of the surface obtained by rotating the curve abo = V7 - x, 1<x< 7

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Q: Use the parametric equations of an ellipse, x a cos(0), y = b sin(0), 0 seS 2n, to find the area…

A: Given that the parametric equation of an ellipse is  x= a cos(θ) , y=b sin(θ) , 0≤ θ ≤ 2π . Here we…