3) Evaluate the double integral Sla dr dy where D is the region bounded by the hyperbolas ry = 2, ry = 4 and the parabolas y? = x, y? = 3x.

Q: Compute volume under the surface x+ 2y2 above the region described by 0sxs1 and 0sysx?, shown below.…

A: Given that surface is x+2y2 and region is described by 0≤x≤1 and 0≤y≤x2. It is required to find the…

Q: Evaluate the double integral [fa² √4 = y² dA, R where R is the region bounded by the circle ² + y² =…

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Q: Calculate the double integral √ √(8x + 2y + 16) dA where R is the region: 0 ≤ x ≤ 1,0 ≤ y ≤ 4.

A: The objective is to evaluate the double integral.

Q: If R is the region bounded by the lines y = x,y=0,x= 1, evaluate the dxdy double integral S by…

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Q: Express the region as a union of Type I or Type II regions and evaluate the integral ffy dx dy. YA 1…

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Q: Consider the integral lo z dxdydz, where the region 2 is located in the first octant and bounded by…

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Q: Use Green's Theorem to evaluate the line integral Icov for the given path. (y-x) dx + (2x - y) dy C:…

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Q: 2) Calculate the integral the regions descri bed. over / 2x- 5xy- 3y² dA. On a y = (x-1) /3 , y= -2x…

A: Bounding lines y=x3         → 3y-x=0y=(x-1)3→3y-x =-1y=-2x    →y+2x=0y=1-2x  →y+2x=1

Q: 4. Finl the volume bounded by the surfaces z x2 and z 4-x2-y2.

A:

Q: Use Green's Theorem to evaluate the line integral Scox (y - x) dx + (2x - y) dy for the given path.…

A: The given integral is                                    ∫Cy-xdx+(2x-y)dy for the given path.…

Q: Sketch the region R whose area is given by the iterated integral. 16 – y2 dx dy 3 2- 2 6 8. 10 12 14…

A: option B

Q: Verify Green's theorem in plane for (x* - 2xy)dx + (x°y+ 3)dy where c is the boundary of the region…

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Q: 2. Find the area of the plane region bounded by y = 3x + 1, x = 1, x = 3,and the x-axis. y y = 3x +…

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Q: 5. Show that, in the region bounded by y = Vx and y = x2 the following double integral 3 (х + у) dA…

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Q: Calculate the double integral ∬Rdxdy, where the region R is bounded by the parabolas y2=2x, y2=3x…

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Q: Use Green's Theorem to evaluate the line integral. y2 dx + ху dy C: boundary of the region lying…

A: Use green s theorem

Q: 2. Calculate the double integral 2ry dA, where R is the triangular region with vertices (0,0), R (1,…

A:

Q: set up the double integral for the area of the portion of the paraboloid z=x^2+y^2 that is between…

A: z=x2+y2∂z∂x=2x∂z∂y=2y

Q: Consider the region bounded by the Xxy curves J 3-2x, and y=3, %3D

A: Calculating the area of the region bounded by the curves

Q: Evaluate  DOUBLE integral xy dA, where D is the region bounded by the line  y = x − 1 and the…

A: Given: The bounded regions are, Find the points where the bounded regions intersect. Substitute…

Q: Use Green's Theorem to evaluate the line integral. √y² dx + xy dy C: boundary of the region lying…

A: We have to evaluate the integral.

Q: Prove that: 1- Cos (2) dxdy (¹) where R the region bounded by x+y=1,x=0.y=0

A: Given integral I=∫∫Rcosx-yx+ydxdy Where R is bounded by x+y=1x=0y=0

Q: Let f(x,y)=|x|+sin (2x−3y). If R is the region bounded by the quadrilateral of vertices (0,3),…

A: We have to find the given integral according to the given region

Q: Use Green's Theorem to evaluate the line integral (y – x) dx + (2x - y) dy for the given path. C:…

A: Use greens theorem

Q: Set up an integral for the surface area of the part of the paraboloid z = 1 - x2 - y2 that lies…

A:

Q: Sketch the region R whose area is given by the iterated integral. dx dy 21 1.5 1.5 y 1- y 11 0.5…

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Q: Sketch the region R whose area is given by the iterated integral. 8 (64 - y2 dx dy 60 8. 50- 6- y 4…

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Q: Use Green's Theorem to evaluate the line integral $. (x2-y2)dx + (2y -x)dy where C consists of the…

A: We will plot the region bounded by two given curves and find the integral using Greens theorem

Q: Use Green's theorem to evaluate the integral: 6(-x²y)dx + xy°dy where C is the boundary of the…

A: Let C be a positively oriented, piecewise smooth, simple, closed curve and let D be the region…

Q: 3. Determine the valume of the solid ebtained by rotating the region bounded by y=x² and x =y2 about…

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Q: If 'V' is the region bounded by the planes x = 0, x = 2, y = 0, z = 0 and z+y = 1 then the value of…

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Q: 2. Find the centroid of the region bounded by the parabola y=x² and the line y=4.

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Q: Evaluate the double integral. 8y2 dA, D is the triangular region with vertices (0, 1), (1, 2), (4,…

A: we have to find given double integral

Q: ydV, E

A: We will draw a region first, then will find limits

Q: Verify Green's theorem in the plane for S(3x² -8y )dx +(4y-6xy)dy, Where C is the boundary of the…

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Q: Sketch the region R whose area is given by the iterated integral. r 64 - y2 Хр хр 6 4 6 2 4 10 20 30…

A: Given integration is, ∫-88∫064-y2dxdy The region of integration is bounded by, x=0, x=64-y2, y=-8,…

Q: Evaluate 2x dV Over the region E bounded by the parabolic cylinders y = x2 and x = y² and the planes…

A: Consider the parabolic cylinders y=x2 and x=y2 and the planes z=0 and z=x+y

Q: Set up and evaluate the integral JJS, ze-(x+y<+z-) dV where Q is the region above the xy-plane…

A: ∫∫∫Qze-(x2+y2+z2)dvQ=x,y,z| hemisphere of radius 5 above XY planeXY- plane ⇒z=0Convert to spherical…

Q: 3. Sketch the region R defined by 0 <y < 8, ty <¤ < y!/3, then integrate dædy R

A: The region R is defined by 0≤y≤8, y4≤x≤y13the figure of R is

Q: Use Green's Theorem to evaluate the line integral Jo for the given path. C: boundary of the region…

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Q: Use Green's Theorem to evaluate the line integral (y - x) dx + (2x - y) dy for the given path. C:…

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Q: If, in an integral triple, we have a D region bounded by the surfaces z = 2x² - y² and z = 9 - 2x² +…

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Q: Apply Green's Theorem for a curvilinear integral 6 y²dx + x² dy in a region B bounded by the lines…

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Q: 4. Set up an iterated double integral equal to the volume of the solid in the first octant bounded…

A: The region is

Q: 8) consider the region R in the first quadrant(xz0, y2) bounded by x=2y² X=Y²+1 a) set up, but clo…

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Q: Evaluate the triple integral. 5z dv, where E is bounded by the cylinder y2 + z2 = 9 and the planes x…

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Q: Evaluate the double integral Jª R where R is the region bounded by the lines y = x and y = 2 and the…

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Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.