Find the centroid (¤, y) of the region bounded by: 52? + 6х, у — 0, х —D 0, and x = 9

Q: S(z,9) = z² + y*;z = f + P;y =P +° , % att = 1 equals Select one: Oa 0 Ob -1 O. 164 Od. 64

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Q: A particle is under the influence of the force F= (-cosh (4x4) + xy)i + (e-y + x)j. The corner…

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Q: Find an upper triangular U (not diagonal) with U2 = I which gives U = u- 1.

A: Given, U2=I

Q: SLo(xy) dA where R is bounded by 9x2 + 4y² = 36 %3D Use the transformation: x = 2u and y = 3v

A: The given region R is: 9x2+4y2=36...(1) To use the transformation: x=2u,y=3v So, equation (1)…

Q: Evaluate X J₁ sin (y + 2 x R where R is the triangular region with vertices (0,0), (0, 1), and…

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Q: Find curl (7z i + 8xj+2y k). curi (7z i+ &x j+ 2y k) = (1 i+( j +( )k

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Q: 1. Let F(x, y,z) = (x + y², y + z²,z + x²). Let C be the triangle with vertices (1,0,0), (0,1,0),…

A: Consider the provided question,

Q: The region W lies between the spheres x² + y² + z² = 4 and x² + y² + z² = 16 and within the cone z =…

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Q: Evaluate [[ 4.ry² — 5x + 5y³ dA over the rectangle R = {(x, y) : -1 ≤ x ≤ 2 and − 1 ≤ y ≤1}.

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Q: Sį : -8(y – 2) = (x – 1)² S2 : y + z = 2 S3 : x = 0 S4 : y = 0 S3 : z = 0 %3D

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Q: Use the map G(u, v) = a = 4, b = 8, c = 6. b J D a y=cx uv v+1' v+1 (x + y) dx dy = to compute f (x…

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Q: a) let f(x, y) = c, ceR and N = (3,5) x (1,4). calculate the area %3D of the graph of f :N→R. a): b)…

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Q: If F(x, y, z) = 10yzi + 10xzj + 10xyk, find div F and curl F. div F =

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Q: ntegrate ze²² dz where C from 1 along the axes to i C

A: (.)   Given integral is,    where  along to the axes to .(.) If a function is analytic then integral…

Q: Find the area +6 C1 R -6 +6 C2: 4x2 + y² = 16 -6 using green's theorem.

A: We are given the above region of which we need to find the area and as per the instruction, we need…

Q: Consider the points A(2, –3, 4), B(4, –5, 1), C'(-2, –4, 1), and D(4, 2, –6). (a) Find the volume of…

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Q: Compute the line integral: y² dx + x² dy two ways. C

A: We have an line integralTo evaluate the line integral by two methods (a) By  Green theorem(b) By,…

Q: find the area of triangle between V and W YA (1, 1, 1) V W

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Q: s) Given u(r, s) =r2 - 2s2, wheter= and s = y? - r, compute for du

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Q: Find J(u, v) if x = u + v, y = 2v.

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Q: et F = t+3 2i-fj+3t°k and G = e'i – 3f j+ e²* & %3D

A: Given are two vector functions F=t+3ti-t2j+3t3k and G=eti-3t3j+e2tk.

Q: Distinguish briefly the Skewness and kurtosis

A: Skewness is a measure of symmetry where symmetry means equal proportion to the left and right to the…

Q: Evaluate z* + x dS where S is the cylinder x2 + y? = 36 between the planes z = -3 and z = 1,…

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Q: || x dA, R is bounded by y = x, 2x + y = 6 and the y-axis. R

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Q: Find /| F-dS if F(x, y, z) = 2xi+2yj+2zk and S is the part of the paraboloid z = = 8-x?-y? lying…

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Q: Evaluate the circulation of G = ayi+zj+ 7yk around a square of side 9, centered at the origin, lying…

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Q: Evaluate // (22 + y?) dA, where R is the region between the semicircles y = v9-x and y = V1- x2

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Q: Evaluate the line integral x²z ds, where C is the line segment from (0,6, 2) to (8, 5, 1).

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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.