a) Evaluate [(2x- y' )dA over triangular region R enclosed between the lines y = -x +1, y = x+1 and y = 3.

Q: Find the area of the surface x2 - 2 ln x + sqrt(15)y - z = 0 above the square R: 1<=x <= 2,…

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Q: 2) Find the centroid of the region above the X is bounded by the Y axis and the line Y =

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Q: Let R be the region bounded by the curve y = r and the line y = 2x. Use inequal- ities to describe R…

A: In this question we have to describe the area of region by using vertical cross section

Q: Compute the area of surface generated by revolving the four-cusped of hypocycloid x⅔+ y⅔ =a⅔ about…

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Q: Sketch the region enclosed by the given curves. y = 3 cos(5x), y= 3 – 3 cos(5x), 0 < x< 1/5 y y 6- 2…

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Q: Let R be the region bounded by y = 5 sin(x , y = 5(x – 2)²,

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Q: Sketch the region enclosed by the given curves. y = 7 cos(TX), y = 12x2 - 3 y y 8 6 4 -1.0 1.0 2…

A: We have to draw the graph and find out the area

Q: Sketch the region R in the XY plane bounded by y=x^2, x=2, y=1

A: Given Functions are y = x2 , x= 2 , y =1

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

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Q: Let R be the region bounded by the curve y = volume of the solid with base R and cross-sections…

A: given curves y=x2+1 and y=-x+3 claim- to find the volume of solid  solution graph of the curve

Q: A solid figure is created by rotating the region R around the x-axis. R is bounded by the curve y =…

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Q: Sketch the region enclosed by the given curves. y = 4 cos(x), y = 4 - 4 cos(x), 0 s xs n y y 4 2 1.0…

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Q: integrate ƒ over the given region. ƒ(u, y) = y - √u over the triangular region cut from the first…

A: Given  The function is ƒ(u, y) = y - √u . The triangular region cut from the first quadrant of the…

Q: express the intergral ∫∫2x dA, as iterated intergral, where R is the region bounded by y=x+12 and…

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Q: Sketch the region enclosed by the given curves. y 2 cos(7x), y = 2 sin(14x), X = 0, 14 y 2.0+ 1.5…

A: We have to find the area between the curves.

Q: Let R be the region bounded by the curve y = x and the line y = 2x. Use inequal- ities to describe R…

A: To describe: The region R using inequalities in terms of its vertical cross-sections. Calculation:…

Q: Evaluate ||xy dA, where R is the finite region in the first quadrant bounded by the R curves y=x²…

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Q: Q1) Find plane area bounded by y = 2,y = 6 – x, and y = 8 - 3x using double %3D

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Q: 4. Find the volume of the solid under the surface f(x, y) = xy and above the triangular region in…

A: .

Q: 7) Use the double integral of a cross product to find the surface area of x = z² + y that lies…

A: Let's find surface area  by using double integral.

Q: The base of a solid is the region bounded by the graphs of y = 3x,y = 6, and x = 0. The…

A: Given, The base of a solid is the region bounded by the graphs of y = 3x,y = 6, and x = 0. The…

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: Find, to two decimal places, the x-coordinate of the centroid of the region in the first quadrant…

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Q: find the ordinate of the centroid of the region bounded by the parabola y = x^2 and the line y = 2x…

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Q: Find the centroid (x¯,y¯)(x¯,y¯) of the region bounded by: y=7x^2+2x,   y=0,   x=0,   and   x=9?

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Q: integrate ƒ over the given region.Quadrilateral ƒ(x, y) = x&gt;y over the region in the first…

A: Given,

Q: Sketch the region enclosed by the given curves. y = tan(7x), y = 2 sin(7x), -77/21 sxs 7/21 y y 3 3…

A: For sketching the region y=tan7x, y=2sin7x, -π21≤x≤π21. Let y1(x)=tan7x, y2(x)=2sin7x, -π21≤x≤π21 We…

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: find the region endlased R by the cunes V=12-2y +1 and Y= -2+2x ャ4.

A: Answer

Q: Find the centroid of the region bounded by the x-axis, the curve y = sec x, and the lines x =…

A: Consider the graph. The graph is symmetric across x = 0.

Q: Determine a region of the xy-plane for which the given differentail equation would have a unique…

A: Given differential equation (y-x) y'=y+x   or    (x+y)dx+(x-y)dy=0 Note that differential equation…

Q: Find the centroid of the region bound by curves y=cosx,    y=0,        x=0,     x=?/2

A: Here given that two curves equation that is y=cosx and y=0 Limite is given that x=0 to x=π\2 Then we…

Q: A region R is bounded by the graphs of y=0.5 Vx and y=0.5x. Find the moments Mx and My of R about…

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Q: (b) Let F = (-yx², xy²). Let D be the annulus 1 < a2 + y² < 4, and let C be its boundary. Evaluate

A: Value of the given integral is

Q: Sketch the region enclosed by the given curves. y = 7 cos(2x), y 7-7 cos(2x), 0 sxs x/2

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Q: It is possible for a region in the xy-plane to be both type 1 and type 2 at the same time.

A: This is possible.

Q: 3.) Find the area of the surface given by f (x, y) = 9 – x2 over the region R: square with vertices…

A: Given: fx,y=9-x2

Q: R is the region bounded by the lines y = x, y = -x, and x = 1. %3D

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Q: Determine the absolute maximum and minimum values of f(x, y) = 2+4x-2.x2+4y-y? %3D on the region R…

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Q: Sketch the region enclosed by the given curves. x = 9y2, x = 4 + 5y2 У y 1.0- 0.5 6. -0.5 o-1.0-…

A: Given curves are

Q: Consider the region enclosed by the curves y = I+1 and y=2x+ 1: %3D

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Q: b. Draw the image of the W-plane into which the region bounded by the straight lines in the Z-plane…

A: The solution is given below

Q: Sketch the region enclosed by the given curves. y = 4 cos(5x), y = 4 – 4 cos(5x), 0sxS a/5

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Q: find the are of the plane region bounded by the urves y=3x2 and y=16-x2

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Q: Sketch the region enclosed by the given curves. y = 8 cos(x), y = 8 - 8 cos(x), 0<x T

A: This question is related to area bounded by curves, We will use integration to solve it.

Q: Verify Green's theorem in a plane | (xy +x²)dx + x² dy, where C is the boundary of the region formed…

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Q: The region in the first octant bounded by the coordinate planes, the plane y + z = 2, and the…

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.