Solve the problem with complete solution and draw the figure. Determine the ordinate of the centroid of the area bounded by the curve x2 = 8y and the line 2x – y = 0.

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: Convert the integral  0∫2 0∫2z y∫2y dxdydz in the order a) dzdxdy b) dxdzdy

A: Given: ∫02∫02z∫y2ydxdydz

Q: 5. Lis the centroid of ANOM. Find ML if ML = 10x- 4 and MR=12x+18. M N. R.

A: Given that :- L is the centroid of NOM   ML = 10x - 4 and Mr = 12x + 18 To find :- ML  By the…

Q: Find the area and centroid bounded by the curve 5y? = 16x and the curve y2 = 8x – 24.

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

Q: Q3: Find the centroid of the next shaded area. 4m

A: Solution :-

Q: Let n ≥ 1 be constant, and consider the region bounded by f(x) = xn, the x-axis, and x = 1. Find the…

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Q: You may recall that the point inside a triangle that lies one-third of the way from each side toward…

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Q: (c) Use Green's Theorem to solve the line integral xy dx + x'dy where C is formed by the parabola y…

A: WE HAVE TO USE GREEN S THEOREM

Q: Q4: Find the centroid of the next shaded area.

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Q: find Ix, Iy, I0, x, and y for the lamina bounded by the graphs of the equations. y = 0, y = 2, x =…

A: The value of I0,Ix,Iy.

Q: The area bounded by the curve y3a and the lines z 4 and a-9 above the z-azis is aquare units O 27v0…

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Q: Locate the centroid x̄ of the area.

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Q: find Ix, Iy, I0, x, and y for the lamina bounded by the graphs of the equations. y = 4 − x2, y = 0,…

A: Calculations: Point of intersection are given by: 4-x2 = 0 =>x2 = 4 =>x = -2, +2 Since, x…

Q: y=x², y = 1, y =9 y=9, first quadrant

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Q: 5. Let R be the region in the first quadrant within the circle z² + y? = 4, outside the circle (z –…

A: Region is in the first quadrant :-    Hence, region the region between these circles in above…

Q: Calculate the double integral (x + y)²ex* - y² dx dy where R is the square with vertices (2, 0), (0,…

A: According to the given information, it is required to find the integral over R where R is square.

Q: The region in the first quadrant is bounded by the curve y = 2 - x^2 and y = x^2. How far is the…

A: Given- The region in the first quadrant is bounded by the curve y = 2 - x2 and y = x2.  To find- How…

Q: Solve the DEs by LT. please show complete slution.   y''' - 3y'' + 3y' - y = x2ex, y(0) = 1. y'(0)…

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Q: 11 10- 9 8 7 6 5- 3 Find the centroid of the region displayed in the graph. (x, y) = 4

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Q: 6) Find the centroid of the region bounded by the curves y = 4x and y = x?. Show how to find the…

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Q: When P = 0 Q2 Shade the area of the region bounded by the parabola, x² + p? – 2(p + 7)x – 5y + 59 +…

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Q: ). Find the centroid of the first quadrant area bounded by the parabola y = x2 and the line y = x.…

A: According to the guidelines answer of first question can be given, for other please ask in a…

Q: Given the curve x = 2 y – y´ and the line x = 0 Find the ordinate of the centroid y of the region…

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Q: Solve the integral. + yz )do; o: part of the plane x + y +== 6 that lies in the first octanct.

A: Solution:

Q: a) Sketch the curve and find the total area between the curve and the given interval on X- аxis. y =…

A: (i) Given curve: y=sinx   And given interval: 0,3π2

Q: Calculates the JR f(x,y)dA bounded by the given region I Loyan dA where the region S is given by the…

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Q: The figure shows the surface created when the cylinder y2 + z2 =1 intersects the cylinder x2 + z2 =…

A: It is given that, the cylinder y2 + z2 =1............... (1) intersects the cylinder x2 + z2 = 1…

Q: The figure shows the surface created when the cylinder y2+z2 = I intersectsthe cylinder x2+z2=1 Find…

A: Given : surface S (say) is created when the cylinder y2+z2=1 intersects the cylinder x2+z2=1 To find…

Q: 2. Let C be the positively oriented boundary of the square whose sides lie along the lines r ±1 and…

A: According to cauchy’s integral formula for any region C,

Q: y 1 X 1 2.

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Q: 4) Find the centroid of the plane region bounded by x2 + y? = 25 and x2 + (y – 6)² = 13.

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Q: 2 (2y-y² 15. Evaluate the integral / x² + y²dzdydx by using cylindirical coordinates.

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Q: Find the generated volume f(x)=sin(x) and the lines x=0 and x=π and rotate about the x-axis V=π^2…

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Q: Evaluate the double integral I2 = || y'dzdy T where T is a triangle with vertices (-4, 0), (0, 1),…

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Q: Evaluate the double integral 2xy dA, where D is the triangular region with vertices (0, 0), (1, 2),…

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Q: Use numerical integration with Ax = 1.0 m to locate the centroid of the surface generated by…

A: Given That : y=3x216 and ∆x=1.0 m To find : locate the centroid of the surface generated by…

Q: 2. The area bounded by y = -(x - 1)2 + 4, and the lines x =1, y = 2, and y = 4 rotated about the %3D…

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Q: =valuate the double integral [2aydA, 2xy dA, where D is the triangular region with vertices (0,0),…

A: Given that a double integration and given  D is  triangular region with vertices (0,0) (1,2) and…

Q: area of the portion of the cylindrical surface y = 4 − x2 in the first octant that is between the…

A: Given: The cylindrical surface is, y=4-x2 ........(1) And the xy-plane is, x2+2x+y-z =4

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: 4. Find the area enclosed by: a. y= sin(x) and y cos(x), x=0, x = and the y-axis. b. y=x and y =Vx.…

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Q: Q4: Find the centroid of the next shaded area. 1m Im 1 Y 1.5m 1m re1

A: Please refer the attached image for complete solution.

Q: Using Green's theorem, convert the line integral §(6y² dx + 2xdy) to a double integral, where C is…

A: Given integral, ∮C6y2dx+2xdy Here C is the boundary of the square with vertices ±2,2 and ±2,-2.…

Q: 2 Find the average height of the paraboloid z = x + y over the square 0<x<1, 0<ys1. The average…

A: Use formula of average height

Q: Given the curve y = x' and the line y = 4x in quadrant Find the ordinate of the centroid y of the…

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Q: The region in the first quadrant is bounded by the curve y = e^x and the lines x = 0 and the x = 1.…

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Q: Find the line integral / (x² + y) í + y³ j ) • d7 where C consists of the three line segments from…

A: The given line integral is ∫Cx2+yi→+y3j→·dr→ where C is the line segment from 7,0,0 to 7,4,0 to…

Q: 4) Using Green's theorem, convert the line integral f(6y² dx + 2xdy) to a double integral, where C…

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Q: Evaluate III Vx2 + y² dV E where E is the region that lies inside the cylinder x2 + y2 = 4 and…

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Q: 5) Using Green's theorem, convert the line integral f.(6y² dx + 2xdy) to a double integral, where C…

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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.