Evaluate the line integral, where C is the given curve; rds; where C:x =t°,y = t, 0

Q: Evaluate the line integral, where C is the given curve. xy dx + (x − y) dy, where C consists of…

A: In the above line integral there are two segments which needto be seperated. First (0,0) to (1,0) so…

Q: Evaluate the line integral y dx +xdy; C is the curve x = 4t, y = t³ – 1, 0sts 1. Jy dx + x*dy (Туре…

A: Consider the provided question,

Q: Evaluate the line integral, where C is the given curve.     C(x/y) ds,

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Q: Evaluate the following line integral along the curve C. (x- y)ds; C is the line segment r(t) = (t,…

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Q: Set up an integral to compute the arc length L of the curve C: r (t) = <글t?, 4t, v2t) from the point…

A: length of arc given below..

Q: Evaluate the line integral, where C is the given curve. (X/y) ds, C: x = t3, y = t,

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Q: Evaluate the line integral, where C is the given curve. Sc zdx + xdy + ydz C: x = t?, y = t^, z =…

A: Solve the given integral.

Q: valuate the line integral, where C is the given curve. z2 dx + x2 dy + y2 dz, C is the line segment…

A: Follow next step

Q: Evaluate the line integral, where C is the given curve C is the line segment from from (0, 0, 0) to…

A: Here   , ds = dx dy dx  Now we  will evaluate the integral

Q: Evaluate the line integral, where C is the given curve. xevZ ds, C is the line segment from (0, 0,…

A: Consider the  line integral ∫Cxeyzds Where C is the line segment from (0,0,0) to (3,4,2).

Q: Evaluate the line integral, where C is the given curve. | xyevz dy, C: x = 2t, y = 4t2, z = 213,…

A: Consider Applying derivative with respect to t,

Q: Evaluate the line integral, where C is the given curve. Sc (2x + 9z)ds C: x = t, y = t2, z = t 3, 0…

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Q: Evaluate the line integral, where C is the given curve. xyeVZ dy, C: x = 4t, y = 3t2, z = 4t³, 0sts…

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Q: Consider the curve defined by the equation xy=25. Set up an integral to find the length of curve…

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Q: Evaluate the following line integral over the given curve C. I) ds; C: r = t², y = 2t, 0<t < 3

A: Surface integral

Q: Evaluate the line integral along the curve C. (xz + y) ds, C is the curve r(t) = (-4 - t) i + 2t j -…

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Q: Evaluate the line integral, where C is the given curve. |x sin(y) ds, C is the line segment from (0,…

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Q: Evaluate the integral ∫Cydx−xdy over the curve C parameterized by r(t)= (cost,sint), 0≤t≤π2.

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Q: Evaluate the line integral, where C is the given curve. (Round your answer to one decimal place.)…

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Q: Evaluate the line integral, where C is the given curve. y° ds, C: x = t°, y = t, osts 3

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Q: Evaluate the line integral, where C is the given curve. 1 ,C:x =t*, y = t", sis1

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Q: Evaluate the line integral, where C is the given curve. ds, C: x = t3, y = t, 0 sts 5 7814.5

A: Here we have to evaluate the line integral, where C is the given curve.

Q: Evaluate the line integral (xy dx + y dy), where C is the curve y = sin(x), 0 ≤ x ≤ π/2

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Q: Evaluate the line integral, where C is the given curve. xyeYZ dy, C:x 2t, y = 3t2, z = 3t, osts1 %3D

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Q: Evaluate the line integral, where C is the given curve. xy ds, C is the right half of the circle x2…

A: C is the right half of the circle x2+y2=16 thus the parameterization of the circle is x=4cos t and…

Q: Evaluate the line integral S, y ds where C:x = t²,y= 2t, 0 <t < 3

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Q: Evaluate the line integral, where C is the given curve. Sc (x + 9y)dx + x² dy, C consists of line…

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Q: Evaluate the following line integral along the curve C. ds, where C is the line segment from (1,1)…

A:

Q: Evaluate the line integral, where C is the given curve. хуеу2 dy, C: х %3D 3t, у%3D 2t?, = 2t3, 0st<…

A: x=3t, y=2t2,z=2t3

Q: Set up an integral to compute the arc length L of the curve C: r (t) = (t², 4t, v/2t) from the point…

A: The given curve is: r(t)=12t2, 4t, 2t From point (0, 0, 0) to point 12, 4, 2 the limit of t is:…

Q: Set up an integral to compute the arc length L of the curve C: r (t) = (t, 4t, V2t) %3D from the…

A: It can be found by integrating between limits of t= 0 to 1

Q: Evaluate the line integral ∫Cx2ds, where C is a the curve given by the equation y=f(x)=lnx, 1≤x≤e.

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Q: Given that C is the curve r(t) = (cos t, t), for /2 sts T, convert the line integral | ds to an…

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Q: Evaluate the line integral along the curve C. (y + z)ds, C is the straight-line segment x= 0, y =…

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Q: Evaluate the line integral along the given paths. y?) ds + (a) C: line segment from (0, 0) to (8,…

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Q: Evaluate the line integral, where C is the given curve. ∫(with c in subscript) x sin y ds, C is the…

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Q: Evaluate the line integral x° + y) ds C Where C is given by r(t) = 3ti+t°j for 0<t<1

A: The region C is given by: r(t)=3t i + t3 j  ;       for  0≤t≤1

Q: Evaluate the line integral, where C is the given curve. z2 dx + x2 dy + y? dz, C is the line segment…

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Q: Evaluate the line integral, where C is the given curve. ∫ c xyeyz dy, C: x= t, y= t2 , z = t3, 0…

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Q: Evaluate the line integral Sp(xi+ yyj) · dr where D is the oriented curve shown below. (1,1) y = x²…

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Q: Evaluate the line integral, where C is the given curve. xy ds,     C: x = t2,    y = 2t,    0 ≤ t…

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Q: Evaluate the line integral, where C is the given curve. z? dx + x2 dy + y² dz, C is the line segment…

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Q: Evaluate the line integral, where C is the given curve. Jo xy ds, C is the right half of the circle…

A: Solved below.

Q: valuate the line integral J xev% ds where C is the line segment from > (1, 1, 1). This yields:

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Q: Evaluate the line integral, where C is the given curve. (4x + 18z) ds, C: x = t, y = t2, z t3, 0sts1

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Q: Evaluate the line integral, where C is the given curve. dy, C is the arc of the curve y = Vx from…

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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 the line integral, where C is the given curve ʃc (x+9y)dx +x2dy, where C consists of line…

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Q: (2x + y)dx + (x + 2y)dy

A: Given integral is:  where C is any curve that joins the point (1,1) with the (2,2).

Q: Evaluate the line integral, where C is the given curve. x sin(y) ds, C is the line segment from (0,…

A:

Arc Length

Arc length can be thought of as the distance you would travel if you walked along the path of a curve. Arc length is used in a wide range of real applications. We might be interested in knowing how far a rocket travels if it is launched along a parabolic path. Alternatively, if a curve on a map represents a road, we might want to know how far we need to drive to get to our destination. The distance between two points along a curve is known as arc length. 

Line Integral

A line integral is one of the important topics that are discussed in the calculus syllabus. When we have a function that we want to integrate, and we evaluate the function alongside a curve, we define it as a line integral. Evaluation of a function along a curve is very important in mathematics. Usually, by a line integral, we compute the area of the function along the curve. This integral is also known as curvilinear, curve, or path integral in short. If line integrals are to be calculated in the complex plane, then the term contour integral can be used as well.     

Triple Integral

Examples: