Sketch the region bounded by the following curves and etermine the centroid of the region. y = 4x2 and y = 4x3 3 48 а) О 14' 25 b) O 48 3 c) O (25 7) 48 3 d) O 25' 14 3 24 e) O 14' 25

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A: Given: let R be the region bounded by the curve y=x3, y=5 and x=2 To find: what is the volume of the…

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A: Graph the given functions using graphing calculator. Shade the bounded region. The region will…

Q: Find the volume of the solid obtained by rotating theregion bounded by the given curves about the…

A: y2=x   ⇒ y=xx=2y  ⇒ x2=yVolume =π ∫abRx2-rx2dy&   , y2=2y ⇒ y2-2y=0  ⇒ yy-2=0   So , y=0,2

Q: Sketch the region enclosed by the given curves. y = 2/x, y = 8x, y = x > 0 y y 6F 5- 5- 4 4. 3 2 1 1…

A: Given equations: y=2x. . . . . (1)y=8x . . . . . (2)y=18x . . . (3)x>0 Explanation: First we…

Q: Let T be the first-octant solid region bounded by the graphs of the equations y = 5(x2 + z?), y = 5,…

A: Given that T is the first-octant solid region bounded by the below equations: y=5x2+z2y=5y=45z=0x=0…

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A: Solution is given below:

Q: 3.find the volume of the region bounded by the surface y=x^2,y+4x+5 and the plane z=0 and z=4

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Q: Sketch the region bounded by the given curves, then find the centroid of its area. 1. x = 8 – y? , x…

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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 enclosed by the given curves. y = 2/x, y = 8x, y = x > 0 y y 6F 5 3 4 3 y 6F 5 3 4…

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Q: The geometric center of the region bounded by the curves 5y²-16x=0 and y²+8x=24 on the first…

A: The given answers do not match the actual answer. Please check the options.

Q: Find the volume of the wedge-shaped region (Figure 1) contained in the cylinder x2 + y? z = x and…

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Q: Sketch the region enclosed by the given curves andfind its area.   y  = 1/x,  y =x ,    y =1/4x  ,…

A: y  = 1/x y =x     y =1/4x and x>0 Formula: Area enclosed between the curves y=f(x) and y=g(x) on…

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Q: Sketch the region bounded by the given curves, then find the centroid of its area. 1. у%3D х*,…

A: (5) From Symmetry we can see that centroid of the bounded region is at (0, 0)

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A: Note:" Since you have posted multiple question. As per our guidelines we are supposed to solve only…

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A: Given: the sphere r=2a cos theta , cone ϕ=α0<α<π2

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A: To find the volume of the wedge shaped region on the figure contained in the cylinder x2+y2=9 and…

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A: We can find the volume by rotation of this curve using washer method.

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A: We will use the cylindrical coordinates to find the required volume.

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Q: 4. y= 6x -x², y = x² – 2x , y = -1

A: Given that     y = 6x-x2 , y=x2-2x , y=-1 Here we have to find the volume and the centroid.

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A: Given:

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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…

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A: Find the limit of the x, y and z:

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A: Find the volume of the solid obtained by rotating the region bounded by the given curves  about the…

Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the…

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Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the…

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A: Area of region bounded by curves

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A: To find the volume using cylindrical coordinates.

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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.