The integral that represents the arc length of the curve y = Inx from the point (e, 4) to the point (e, 5) is: A) Inz+1 da InrV+1 B) ſ v+1 dr C) [, v241 dr D) S, Vr² + 1 dr E) S yVu +1 dy

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A: Thanks for the question :)And your upvote will be really appreciable ;)

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A: Green's theorem defines that : for ∮CPdx-Qdy there is an integral exists of ∫D∫∂Q∂X-∂P∂Y.dA Here,…

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Q: The foilowing describes a para bolic path C: Pt) = (t, 2, 1-t?) %3D if F = (32, x + y+Z, 2x >,…

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Q: Let S be the torus parametrized by G(e,p) ((a bcos(p)) cos(0), (a +bcos(p)) sin(0), bsin(p)) for θ,…

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Q: Use Green's Theorem to evaluate . ydx – xdy where C is the cirde centered at the origin

A: Given integral ∮Cydx−xdy, where C is the circle centered at the origin with radius 4 We have to find…

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Q: Evaluate the cylindrical coordinate integral: L L dzr dr de O 647 O 87 O 167 O 1287

A: To solve the integral

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Q: . Calculate the flux integral fF.n ds, where C is the positively oriented circle of radius 1…

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A: Use parametric to solve

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Q: y*dx + x*dy = (N, – M,) • dA (м, - м,) ал

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A: We will first parametize the circle C

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

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Q: 3. Please give clear explanations

A: The parametrization of a surface S is given by       G(u, v)=(u, v, uv) where D is u2+v2≤1.

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A: Let us assume thatC1:x2+y2=1Put x=t,y=1-t2 and z=0.Hence,dx=dtdy=-t1-t2dz=0and 0≤t≤1.Let C2:The line…

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A: Here we solve the given problem of integral.

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Q: Sketch the grapm of the pare cone (6) and Sketeh TE) and valve of f. quaph N't) at the %3D

A: For a vector valued function r→t=a(t)i→+b(t)j→, its unit tangent vector T→t and unit normal vector…

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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.