Determine the y-coordinate of the centroid of the shaded area. y Ix= y2/b 0.48b b Answer: ỹ =

Q: What is the x centroid position for the shape below? Center:D, 2m 10m 3.4m 3.9m 4.4m 4.9m

A: Formula for centroid, C C=∑Ax∑A

Q: + y? )dx + (x² – y²)dy , where C is the triangle with vertices (0, 0), (2, 1), and (0, 1), sitive…

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Q: Find the area of the surface. The portion of the cone z = 4V+ y² inside the cylinder x? +y² = 16

A: Consider the provided cone z=4x2+y2 inside the cylinder x2+y2=16. Find the area of the surface. The…

Q: Ex4: Find the centroid of the region that lies inside the cardioids r = a(1+ cos8) and outside the…

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Q: Find the surface area generated by rotating the given curve about the y-axis. x = e' - t, y = 4e/2,…

A: *to find:- surface area, when rotating about y axis.

Q: y=x¯, y= 2x

A: We can find the centroid using the required formula as below

Q: x² + y? that is below the plane Find the surface area of that portion of the paraboloid z = z = 2.

A: Given paraboloid z=x2+y2 Surface area, AS=∫∫R∂z∂x2+∂z∂y2+1dA AS=∫∫R2x2+2y2+1dA…

Q: Find the paint the Surface Z = I+ xy thet is hearest on to the origin ·

A: Lagrange multipliers are used to find the local maxima and minima of a function under certain…

Q: Find the area of the surface generated by revolving the curve about the indicated axis. y = x3/9, 0…

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Q: Calculate the y-coordinate of the centroid of the shaded area. 66 mm Answer: y = y i | 27 27 → mm mm…

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Q: Locate the centroid x̄ of the area.

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Q: Determine the area of the surface with parametric equat ions x = 2u?, y = v², z = 2uv, %D 0<u< 3, 0<…

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Q: Find the surface area of the solid obtained by rotating the curve 0 <y<1 about the y-axis. 3 a) c)-…

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Q: Find the area of the surface that is generated by revolving the portion of the curve y= X between x=…

A: We can solve as follows

Q: How far is the centroid from point A? У-аxis - 25 cm - 30 cm 25 cm 30 cm 40 cm 25 cm - 30 cm 50 cm…

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Q: Use cylindrical coordinates to evaluate V9-x² r9-x²-y² a² dz dy dx -3 J- 9-x² Jo Do not forget to…

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Q: Find the average height of the paraboloid z = x + y over the square 0sxs2,0sys2. The average height…

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Q: Determine the surface area of the solid obtained by rotating y=v9-x from -2sxs2 about the x-axis. A…

A: Area of surface generated by rotating a curve y=f(x) from x=a to x=b about x-axis  A=∫ab2πydsWhere…

Q: Find the surface area obtained by revolving the parabola x? = 4y from x = 0 to x = 2 about the…

A: If a curve f(y) is revolving about the y-axis over the interval [a,b], then the surface area is:…

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: Q2. Evaluate , e5xy dA, where R is the region enclosed by the lines y =;x and 2y = x 2 and the…

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Q: Find the surface area of the object obtained by rotating y = +÷, 1 1<x<2 about the x-axis.

A: To find the surface area of the object obtained by rotating y=x36+12x ,  1≤x≤2 about x-axis.  Let,…

Q: Determine the y-coordinate of the centroid of the shaded area. bl x=y²/b 0.62b b Answer: y = i b

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Q: Calculate the moments of inertia (Ix and Iy) of the shaded area given in the figure with respect to…

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Q: Determine the y-coordinate of the centroid of the shaded area shown. 18" Parabolic 2" 9"

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Q: HW: Find the area of the surface generaled by revolving 3DVy, 1 <y<8 about the X- axis. 1. 3.

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: a) Find the surface area of the object obtained by rotating x = e2y , –1 <y <1 about the y – axis.

A: We have to find the surface area of the solid obtained by rotating the curve x=e2y about the y-…

Q: Find ʃR (x2 + y2) dA where R is the region 4 ≤ (x2 + y2)≤ 9. Hint: Use polar coordinates.

A: The given integral is,

Q: Find ʃR sqrt((x2 + y2)) dA where R is the region 4 ≤ x2 + y2 ≤ 9. Hint: Use polar coordinates.

A: Given double integral is,

Q: Use your grapher to find the surface's area 3) y = sinx, 0 s x < T/4; x-axis A) 5.46 numerically. B)…

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Q: Determine the y-coordinate of the centroid of the shaded area. bl. | x=y²/b b Answer: y = i 0.48b MI…

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Q: Q:3: a) Find the surface area of the object obtained by rotating x=e2y, -1sys 1 about the y-axis.

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

Q: Q1. Locate the centroid of the shaded area shown in the Figure (1). y = 4vx -27 2 mm 9 mm 6 mm…

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Q: Q3. With respect to the coordinate axes X and Y locate the centroid of the shaded area as shown in…

A: As according to given diagram: Area of trapezoid is: A=100×220+12×220×50A=22000+5500A=27500 mm2…

Q: Use sine and cosine to parametrize the intersection of the surfaces x² + y² = 16 and z = 4x³. r(t) =

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Q: Find the moment of inertia of the plane area generated by the equations y = 8x³, y = 0, and x = 1…

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

Q: Find the Centroid tor the Shaded area. [Q2] 120 r=5 150 6 30 90 130

A: Solution to Question (1) Given a shaded area with dimensions,we have to find the centroid of that…

Q: Determine the y-coordinate of the centroid of the shaded area shown. 16" Parabolic Y 3" 0 I Answer:…

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Q: Find the area of the surface of rotation created y = /2x – x2; <a< by rotating this curve around the…

A: By using area of surface formula, we calculate the required area of surface.

Q: Find the area of the surface obtained by rotating the curve y = Vx on the interval [0,1] around the…

A: The equation of the curve is y = x3 = x13 To evaluate: The area obtained by rotating the curve on…

Q: Find the area of the surface that is generated by revolving the portion of the curve yx' between x0…

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Q: Find the area of the part of the surface ¤= (y/2 + z3/2) with y E [0, 2] and z E [0, 2]. Area =

A: For the solution of the problem follow the next step.

Q: Determine the y-coordinate of the centroid of the shaded area shown. 11" Parabolic - 3" 6" Answer: ỹ…

A: We need to find y co-ordinate of centroid.

Q: Jind the Surface area of the part of the para boloid 2=X+y" lyrng Orer the regron R

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Q: V1+ e" about the Calculate the surface area of the solid obtained by rotating the curve y x-axis for…

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Q: Evalute ff Rx²dA, where R is the region in the first quadrant bounded by the hyperbola xy = 16 and…

A: The given integral: ∫∫Rx2dAWhere R is the region in the first quadrant bounded by the hyperbola…

Q: Q2. Evaluate , e5xy dA, where R is the region enclosed by the lines y =x and 2y = x 2 and the…

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Q: Find the centroid of the fourth quadrant area bounded by the following curves y? + 2y + 8x =-1 and y…

A: We will use double integration to solve this

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

A: IN THIS QUESTION WE HAVE TO FIND AREA FROM REVOLUTION OF A ELLIPSE.

Q: Find the area of the surface that is generated by revolving the portion of the curve y = x between x…

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.