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

Q: The length of the curve defined parametrically by: x = e*cost, y = e' sint, 0 Sts is equal to:…

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Q: = V4 cos" : – 1, y = 10 < x < 30

A:

Q: nd [(dy)/(dx)] if the curve is defined by 7 x? e7y + 6 y² e² x

A: We are asked to find the derivative

Q: Evaluate y+z) ds along the curve r(t) = 2ti + tj + (4 – 2t)k, 0sts1.

A:

Q: Let m be a positive real number and C be the curve given by: r(t) = m(-cost + 3)i – m(sint + 3)j+…

A: If r(t) = (f(t) , g(t) , h(t))then L = ∫ab r→'(t)  dtwhere  r→'(t)  = f'(t)2 + g'(t)2 + h'(t)2

Q: Evaluate S. x?dz + z?dy + y?dx where C is the curve x = t2 ,y = t², z = t² from t = 0 to t = 2.

A: We will use concept of line integral to solve this.

Q: 13.3. Let y be the curve given by z(t) = t + it?, 0<t < 2T. Evaluate |z|²dz.

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Q: (b) The curve y = x +3x, from x 1 to x = 3 (c) The ,2 1 from 2 to g

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Q: Evaluate [(x +2y) ds, where C is the curve defined by y = √√4 – æ², for x = [0, 1

A: Here ds is arc length.

Q: Compute f ds for the curve specified. f(x, y, z) = 2x2 + 8z, c(t) = (e*, t², t), 0 sts 1

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Q: Compute f ds for the curve specified. f(x, y, z) = z2, r(t) = (2t, 3t, 4t) for 0 <ts 2

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Q: d'y Consider the curve y = ry+ 1, What is the value of at (0, 1)? dz

A: Given curvey2=xy+1

Q: dy Find for the curve 49 + 6x° = 3 + sin(7x-y). da

A:

Q: Sketch the curve by eliminating the parameter, and indicate the direction of increasing t at t = 0.…

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Q: 10. If the curves f(x, y) = 0, y, z) = 0 touch, show that at the point of contact, dr dø dr dø dy dx…

A: According to our guidelines, we can answer only the first question, the rest can be reposted.

Q: At the given point, find the line that is normal to the curve. 2x y-cos y 3x, (1,x) 1 O A. y= -7**7…

A: The given curve is 2x2y – π cosy = 3π and the point is (1, π). Evaluate the slope of the tangent to…

Q: (d) The curve y = x – x² from r = 0 to r = 2

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Q: Set up an intergral for the length of the curve, 04X y%3DZE* sin cx), O4 XE

A: Explanation of the answer is as follows

Q: The Normal to the curve 2x2 – y? = 1 at the point (1,1) is: %3D 3 y =-*+ y =x+ y = 2x + 1 %3D P. y =…

A: To find The equation of normal to the curve 2x^2-y^2=1 at the point (1,1)

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

A: 9

Q: 2tź from t = 0 tot = 1. 3 t°, y = 9. Find the length of the curve defined by x = %3D %|

A: Length ‘L’ for the curves in parametric form can be given by the formula mentioned below as. Then…

Q: = fx x²zdx- dx − yx² dy + 3 dz along the curve C shown in the figure. - Z 2 2 [x²zdx - yx² dy + 3 dz…

A:

Q: 19. Evaluate Scx ds, where C is a. the straight-line segment x = t, y = t/2, from (0, 0) to (4, 2).…

A: Part (a)

Q: Let y be the part of the curve y = x² running from (-1,1) to (2,4). Calculate xy dx + (x + y) dy.

A: (1)

Q: dy Find for the curve x-2.x'y-20y 2 at point (-2,1). de

A:

Q: 23. Evaluate x² c ¥4/3 ds, where C is the curve x = t², y = t°, for 1st< 2.

A: Given curve is

Q: Evaluate ∫C x ds, where C is the parabolic curve x = t, y = t2, from (0, 0) to (2, 4).

A: Given: Parabolic curve x=t, y=t2 from (0,0) to (2,4)

Q: Find the length of the curve. x=(y - 1) 3/2 from y = 1 to y = 4 O 7 O 10 21 2 O 1

A:

Q: Compute f ds for the curve specified. f(x, y, z) = 2x? + 40z, c(t) = (5e", 5t2, 5t), 0sts 1 %3D

A: Use parametric to solve

Q: 1. Let y be the part of the curve y =r² running from (-1,1) to (2,4). Calculate ry dr + (x+ y) dy.

A:

Q: The length of the curve defined parametrically by: x = e'cost, y = eʻsint,0 <t <, is equal to:…

A: given parametric curve x=etcost     y=etsint

Q: Let C be the curve y = x³ – 3x2 + 4x – 1 joining the points (1, 1) and (2, 3). Find the value of…

A: We need to find value of integral.

Q: Find all values of t for which the curve given parametrically by x(t) = 4+ 2t2 y(t) = 212 + t3 , is…

A: Explained below

Q: O Find the length of the following curves 4/2 3/2 + Dx, 0<I<1, 3 i) y(r) = 21 ii) 1 = ² + 21, y=…

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Q: Can there be a curve satisfying the following conditions? d2y/dx2 is everywhere equal to zero and,…

A: To check: The curve satisfying the given condition or not.Explanation:

Q: The length of the curve defined by x =(v² + 2)E, y € [0,1]. Select one: none O 12

A: Arc length of the curve x=g(y), y∈[a, b] is, S=∫ab1+(g'(y))2 dy

Q: |Verify that Green's Theorem is true for S,3(y2 – x) dx + (x² – y)dy given that the curve C is…

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Q: For the curve x=3cos(t), y=4sin(t), find the value of d^2y/dx^2 at the point where t=π/5.

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Q: Compute f ds for the curve specified. f(x, y, z) = z2, r(t) = (2t, 3t, 4t) for 0 sts 2

A:

Q: Compute f ds for the curve specified. f(x, y, z) = x²z, r(t) = (3e*, 2/6t, 4e-t) for 0 sts1

A: Given:

Q: (b) Verify that Green's Theorem is true for S,3(y² – x) dx + (x² – y)dy given that the curve C is…

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Q: Consider the curve x²y + y²x = 6 A) Find in terms of x and y dx

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Q: Find the length of the curve r(t) (1,t²,), 0sts1 %3D «3 Ost<1

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Q: What's a parameterized version of the curve given by y - 3 = x + sin x? A. y = -3t, x = y+ sin t…

A: The equation of the curve is y-3=x+sin x. That is, the equation can be rewritten as, y=x+sin x+3.

Q: IF=(x+y)i+(y– )j+z?k over the curve r(t) = (t²,t²,t*), 0sts1

A:

Q: py*(1 + x*)dx + 2ytan xdy ,where C is closed curve xi +yi = 1

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Q: Evaluate | 9+x* dx+xy*dy along the positively oriented curve C where the C is the boundary of the…

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Q: Evaluate c (xy + y + z) ds along the curve r(t) = 2ti + tj + (4 – 2t)k, 0st<1.

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Q: Let y(t) = (1/2)te*/2, 0<t< 2n What is the terminal point of the curve? — 2п

A: Terminal point of curve is obtained at terminal point of path.

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.