Let C2 be the curve defined by R(t) = (t² +t + 3, 4t – 5, 2+ t – t2), t e [0, 1]. %3D | (x + y+ 2) ds. C2 Evaluate

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Q: 21 Let F(x, y) = (3x + 2y)i + (2x - y)j. Evaluate F. dr where C is the curve X y from (0, 0) to (1,…

A: Here we calculate the integral along the curve x = y2 from (0,0) to (1,1)

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A: We wil first equation of parametric equation of line segment

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Q: Evaluate fxds, xds, where C is the curve r(t) = (2+t)i+(t) j+(5−3t)k, 0≤t≤1

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Q: Draw a picture on the z-plane

A: In this question, we draw a picture of the given curve in C(t). here, first, we write the real and…

Q: a. Find a function (f(x,y,z)) such that (F = Vf(x,y,z))? b. Use part (a) to evaluate (F. dr ) along…

A: We have to evaluate the ∫CF.→dr→.

Q: b) Evaluate S(2y + 4z)dx + (2æ + 3z)dy + (4x + 3y)dz, where C is the curve given by r(t) = for 0 <t…

A: given ∫C2y+4zdx+2x+3zdy+4x+3ydz where C is the curve given by rt=t3,2sinπt2,3cosπt2 for 0≤t≤1…

Q: Let 7(t) = (- 2t³ – 3, t2 + t, - 4t2). Find the line (L) tangent to 7 (t) at the point (- 19, 12, –…

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Q: Q2: Evaluate . f ds where C is the given oriented curve r(t) = (-2 + 6t ,5 + 8t) for (0 <t< 1) and…

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Q: Consider the curve defined by t and y = 2t² +6, for -2 ≤ t ≤ 3. Find an equation in x and y whose…

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Q: Q. (a) Find an equation of the tangent plane to each surface at the given point. (b) Find symmetric…

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Q: r(t)=(-6–2t)i+tj– 2tk, 0<ts Evaluate where C is the curve given by C

A: Solve the following

Q: If C is a piecewise smooth curve from (1,2, 3) to (4,5,6), then | . dx + 2 dy + 3 dz=

A: The value of the given function can be found with the help of the integration. Substitution of…

Q: 2. Evaluate [ F C F = (xz, 0, yz) and the path C is the line segment from point (-1,2,0) to (3,0,1)…

A: Given that, Now,

Q: Find F-dX where C is the curve X(r) = r°I+( 2r+ 1J, 0<I55, and Fxy) = rI+yJ.

A: 9

Q: Evaluate |-y dx+x dy , where C consist of the curves along the horizontal line from (-4,4) to (-2,4)…

A: The given integral is: ∫C -ydx+xdy Where C consists the curve along the horizontal line from -4,4 to…

Q: Please review the screenshot and provide a solution. Please make sure that the solution is formatted…

A: Approach: Understand the problem statement:The goal is to evaluate the integral ∫f(x,y,z)ds over a…

Q: (47) Let C be the curve y = 5x where 1 ≤x≤9. Calculate the length of C.

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Q: Evaluate S. (2xy – x²)dx + (x + y²) dy such that c is a curve bounded by y? – x , y – x² ?

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Q: Let C1 be the curve r(x)= (x − lnx )i + (x +lnx )j, 1<=x<=e, and let C2 be the curve of y=et,…

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Q: E.g. Let f(x, y) = x² - 2xy + y². The graph and contour diagram of f is given below right. Compute…

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Q: he curve y = X fc (vî (yi

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Q: Let (t)=(-5t2+4,t³-+4,2+³) 7 Find the line (L) tangent to (t) at the point (-1,0,2) L: (x,y,₁2)= +t

A: The given problem is to find the line tangent to the given parametric curve at the given point…

Q: Compute the length of the curve r(t) = (-4t, 5t — 3, -2t + 3) over the interval 0 ≤ t ≤9 L =

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Q: 3. Evaluate (2ry - )+(r +2:)7+(2y- 2r2)k) - dr, where C is a simple curve from (-3,-2,-1) to (1, 2,…

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Q: Evaluate + 5x)dx + (ye* – 3y²)dy where C is the boundary of the curve given below. -2

A: Detailed explanation mentioned below