Integrate h (x. y.2) = yzi+xj+xzk over the indicated path: the line segment from (0. 0. 0) to (1. 1, 1).

Q: If C is the line segment from (6, 1) to, (0,0), find the value of the line integral: S(5y i+ x) • dr…

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Q: Use Green Theorem to evaluate C P xydx+e'dy where Cis the path from (0,0) to (1,1) along the graph…

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Q: Evaluate the line integral / (x+ 2- rom (0,0) to (3, 0), the path C2 fro co (0,0) by applying the…

A: Consider the provided question, Hello. Since your question has multiple sub-parts, we will solve…

Q: Calculate the line integral f -y²dx + xdy where ŕ is the path y² = 2x − x² such that x>1 and y > 0.

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Q: 2. Evaluate the given line integral, | (-y,x – y) · dR, where C is the line segment from (1,0) to…

A: To find the line integral we use the equation of line segment in parametric form using given points.

Q: compute ∫C F · dr for the oriented curve specified. F(x, y) = (ey^-x, e2x), piecewise linear path…

A: compute ∫C F · dr for the oriented curve specified. F(x, y) = (ey^-x, e2x), piecewise linear path…

Q: Find the line integral ye-xz ds Here, C is the path r(t) = [t,3t,-6t], 0sts In(8) ·

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Q: Use Green's Theorem to evaluate the line integral |v - x)dx + (2x – y)dy for the given path. C: x =…

A: Answer

Q: Integrate h (x. y) xy'i+2j over the indicated path: Brr(u) = (1- u)i. HE [0. 2).

A: Consider the given function and path.

Q: 2. Evaluate the given line integral, (-y,x – y) · dR, where C is the line segment from (1, 0) to…

A: Introduction: The formula of line integral of the function f(x,y) on the line segment C(t) is given…

Q: Evaluate the line integral x +1 ds /1+4x² Vĩ where C is the part of the parabola y = 9 – x² from…

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Q: Evaluate the line integral. [(x - y) ds C: x² + y² = 16 Lox (x - y) ds = C i

A: Evualate the line integral

Q: Evaluate the line integral [x(1 с where C is given by the line r(t) = (1 + 3t, 2t), 0≤ t ≤ 1. x(1 +…

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Q: Show that the line integral | 2.xe- dx + (2y – a²e¬") dy is independent of path and evaluate the…

A: Here we have to show that the given line integral is path independent and evaluate the line integral…

Q: Evaluate the line integral 32xy ds, where C is the portion of the parabola y = x² from (-1,1) to…

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Q: The value of the line integral S(2xy dx + 2x?ydy + dz) C along a path joining the origin and the…

A: We have to find the value of given line integral.

Q: 3. Calculate the line integral S F - d7, where F = (x²y³, x³y?) and C is the path given by C 7(t) =…

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Q: Evaluate the line integral f. (2x – 4xy)dx + 3xy – 2x³y)dy over the straight path L joining point…

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Q: Evaluate the line integral / x°z ds, where C is the line segment from (0, 2,4) to

A: Line integral: - The function to be integrated is determined along a curve in the coordinate system…

Q: Find the path of a heat-seeking particle placed at point P on a metal plate whose temperature at (x,…

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Q: Evaluate I = fc (sin(x) + 4y) dx + (9x + 7y) dy for the nonclosed path ABCD in the figure.

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Q: Let y = 3x + 3x + 2. If Aa = 0.4 at x = 1, use linear approximation to estimate Ay | Ay a

A: We have to find the change in y using linear approximation

Q: Evaluate the line integral fe y dx + x dy where C is the parameterized path x = , y = f, 3 <iS9.…

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Q: Find the path of a heat-seeking particle placed at point P on a metal plate whose temperature at (x,…

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Q: Use Green's Theorem to evaluate the line integral (y – x)dx + (2x – y)dy for the given path. C: x =…

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Q: 17. Integrate f(x, y, z) = (x + y + z)/(x² + y² + z²) over the path r(t) = ti + tj + tk, 0 < a < t<…

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Q: The line integral 2xe" dæ + a²e" dy + (1 – 2²)e¬²² dz is not independent of path.

A: The line integral ∫CF·dr is independent of path if the curl of F is zero, that is, ∇×F=0. Here, The…

Q: Find the path of a heat-seeking particle placed at point P on a metal plate whose temperature at (x,…

A: Let the required path be γt=xti+ytj . Then the velocity vector in the direction of maximum…

Q: Use Green's Theorem to evaluate the line integral √(x - (y - x)dx + (2x - y)dy for the given path.…

A: Let's find.

Q: Evaluate x*dx C + xy dy, where C is the triangular curve consisting of the line segments from (0, 0)…

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Q: Evaluate the line integral cy dx + x dy where C is the parameterized path x = y = t° , 2<t< 6. Scydx…

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Q: Use Green's Theorem to evaluate the line integral (y – x)dx + (2x – y)dy for the given path. C: x =…

A: Given integral is ∫Cy−xdx+2x−ydy where C:x=2cosθ,y=sinθ,0≤θ≤2π. Green theorem is given by…

Q: 2. Evaluate the given line integral, (-y,x – y) · dR, where C is the line segment from (1,0) to…

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Q: Integrate f(x,y,z) = (x + y +z)/ (x² +y² +z? over the path r(t) =t i+tj+3t k, 0<a<t<b.

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Q: Evaluate the line integral. { 4) ( y2 dx + x dy; C is the curve x =t2 - 1, y = 4t, 0 st s 1

A: The given line integral is ∫Cy2 dx + x dy; C is the curve x=t2-1, y=4t, 0≤t≤1

Q: Use Green's Theorem to evaluate the line integra Icon (y − x)dx + (2x − y)dy - - for the given path.…

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Q: Evaluate the line integral di the path over C from to Q(2,4) P(O,) where F(xy) 2xy°2+3y5 13D to ネソーメ…

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Q: Integrate h (x. y) = yi+xj over the indicated path: r(u) = ui+ u²j. ue [0, 1).

A: Given hx,y=yi+xj and ru=ui+u2j, u∈0,1 We have to integrate hx,y=yi+xj along the path ru=ui+u2j…

Q: Evaluate the line integral ∮C x dy−y dx where C is a circular, closed path defined by x^2+y^2=16

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Q: The value of the line integral S(2xy²dx + 2a?ydy + dz) along a path joining the origin and the point…

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Q: 2x dV, where E is bounded by the paraboloid x = 2y2 + 2z2 and the plane x = 2. %3D

A: The given integral is ∭E2xdV. The region E is bounded by the paraboloid x=2y2+2z2 and the plane x=2.…

Q: 3. Show that the line integral | (r + y)dx + xdy is independent of path and evaluate this integral…

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Q: Evaluate the path integral between the points A = (1,3) and B = (2,5) of: B *(x²y + 2y)dy, with y =…

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Q: Find the image of the line z =3 +iy under f(z) = e

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Q: Evaluate the line integral y dx + x dy where C is the parameterized path x = = ² , y = t° , 3 -ydx +…

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Q: Evaluate the line integral ſ. 3(x – y) ds along the path C:r(t) = ti + (2 - t)j, 0<t<1

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Q: Evaluate ∮C(yexy−sinx)dx+ (xexy+ 1)dy where C is the path r(t) given by x=t,y=π/2(t−1)2 from t= 0 to…

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Q: Integrate h (x, y. 2) = yzi+xj+xzk over the indicated path: (a) the line segment from (0, 0. 0) to…

A: definite integrate calculus

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.