Given that C is the curve r(t) = (cos t, t), for /2 sts T, convert the line integral | ds to an ordinary integral. Do not evaluate the integral.

Q: Please evaluate the following line integral: Sc y? dx +2xy dy By parameterizing C as the line…

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Q: Sketch the curve y cu. = x sq.   Use Formulas 3 and 4 to set up two integrals for thearc length from…

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

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Q: Given the integral " Se F(x, y) dydx, which ONE of the following integrals is equivalent?

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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: Let L be the length of the curve x = ln t, y = sin t (1 ≤ t ≤ π) An integral expression for L is…

A: Given the curve x=ln t , y=sint in the interval (1 ≤ t ≤ π) We need to find the integral expression…

Q: Express the arc length of the curve y = x 4 between x = 2 and x = 6as an integral (but do not…

A: Given y=x4 between x=2 and x=6

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 line integral along the path C given by x = 6t, y = 24t, where 0 tS 1. (x+3y²) dy Need…

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Q: Evaluate the integral (+ 2) dz where C is the line segment from the origin to the point 1+ 2i.

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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: Set up an integral to compute the arc length L of the curve C: r (t) = <글t?, 4t, v26) from the point…

A: Concept of arc length.......

Q: Evaluate the line integral along the path C given by x = 4t, y = 8t, where 0 st< 1. + 3у?) dy

A: We need to evaluate the following line integral ∫Cx+3y2dy Where, C is defined as x = 4t, y = 8t ;…

Q: Evaluate the line integral, where C is the given curve.     C xeyz ds, C is the line…

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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: Define the following improper integrals integral - infinity to 0  f(x) dx

A: Given: The improper integrals f(x)dx from limit -infinity to zero.

Q: Evaluate the line integral by the two following methods. y) dx + (x + y) dy C is counterclockwise…

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Q: Evaluate the line integral, where C is the given curve. | xyz? ds, C is the line segment from (-2,…

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Q: Set up an integral that represents the arc length of the function y = 4a4 + 5x from the point (0,0)…

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Q: Evaluate the line integral (x+ 1 ds along the curve C given by r (t) = (2 sint, 2 cost), 0<t<n %3D

A: Given: rt=2sint, 2cost We know that rt=x,y So, x=2sint, y=2cost ⇒dxdt=2cost, dydt=-2sint Also, we…

Q: Evaluate the line integral by the two following methods. $(x- y) dx + (x + y) dy C is…

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Q: Evaluate the line integral along the curve C. [(x+3y)dx + (x-y)dy, C: x= 2cost, y = 4sint, 0≤ts-…

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

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Q: Evaluate the line integral ds along the curve C given by 7()=(2 sint, 2 cost), 0sts T.

A: Given line integral is ∫Cx+12yds. Curve is r⇀t=2sint,2cost,0≤t≤π. xt=2sint,yt=2cost Compute the…

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: Evaluate the following line integral along the curve C. - y)ds; C is the line segment r(t) = (t, 3t…

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Q: Evaluate the line integral - y² dx, where C is the square cut from the first quadrant by the lines x…

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Q: Consider: S (x?, v>dr, C: r(t) = (sint, cost), te[0,1] Which one of the following "regular"…

A: Given ∫Cx2,ydr and C:rt=sint, cost i.e. xt=sintyt=cost

Q: 1+y dy

A: We can solve the given integral as follows:

Q: Evaluate the line integral along the path C given by x = 4t, y = 8t, where 0 s t < 1. dy

A: Given: I=∫Cx+3y2dy And x=4t, y=8t  and 0≤t≤1   As we know that; The Power rule: ∫xndx=xn+1n+1+C

Q: Evaluate the line integral, where C is the given curve. | xyz? ds, C is the line segment from (-3,…

A: Integration

Q: Evaluate the line integral, where C is the given curve; rds; where C:x =t°,y = t, 0<t<1 (ii) ryds…

A: The solution is given as

Q: Use Green's theorem to evaluate the line integral along the given positively oriented curve. | 6y3…

A: given circle x2+y2=4

Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 sts 1.

A: The given integral is ∫c(x+3y2)dy   and the curve C is x=2t,  y= 6t   where 0≤t≤1 Now, y=6t⇒dy =…

Q: Evaluate the line integral along the path C given by x = 2t, y = 8t, where 0 sts 1.

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Q: Evaluate the line integral by the two following methods. (x - y) dx + (x + y) dy C is…

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Q: Evaluate the integral a sin y ds where C is the line segment from (0, 3) to (4,6),

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Q: Suppose we want to find the area enclosed by the curves y1 (z) = sin(z) and y2(z) cos(z) %3D %3D to…

A: We will answer the first question since exact one was not specified. Please resubmit the question…

Q: Evaluate the integral , dx 1+ e* using the substitution u = 1+ e". %3D et dx 1+ e"

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Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 stsi. (y - x) dx +…

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Q: Evaluate the line integral, where C is the given curve. xeV2 ds, C is the line segment from (0, 0,…

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Q: Evaluate the line integral by the two following methods. f (x - y) dx + (x + y) dy C is…

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Q: Apply trapezoidal and Simpson's rules to the integral 1 =[ \1-x² dx h=0,2

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Q: Convert the line integral to an ordinary integral with respect to the parameter and evaluate it.…

A: here we will convert the whole integral into t

Q: Use an appropriate change of variable to evaluate the double integral: co where R is in the first…

A: Given the region:

Q: Express the length L of the curve r = sin3(0), 0 < e < as an integral but do not evaluate it. /7 de

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Q: Use an appropriate change of variable to evaluate the double integral: ソーx COS dA, y+ x R where R is…

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Q: Evaluate the integral. (Use C for the constant of integration.) sin(t) dt os°(t) coS

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Q: Evaluate the line integral, where C is the given curve. C is the arc the curve y = Vx from (4, 2) to…

A: We have to find the line integral of ∫Cx2y3-xdy, C is the arc of the curve y=x from (4,2) to (9,3)