Use Green's theorem to evaluate the line integral I of the one-form W = + æ sin? (y)) dæ + (x² cos(y) sin(y) + xy+sin" (y)) dy along the closed curve in R? formed by going from the origin to the point (T,0) along the arc of the curve y = 8 sin(x), and then back to the origin along the a-axis.

Q: 6. Consider the parametric curve x(t) = 1 + cost+cos 2t, y(t) = sint + sin 2t = sin t(1+2 cos t)…

A: Given that                Then            At  , we need to find the value of .

Q: x(t) = 3 cos t y(t) = 8 sin t 0<t< 2n a) What does the curve described by these parametric equations…

A:

Q: Find y SX a) y = 3 sin (x² + 5x - 3) y' = c) y = sin" (6x) y'= b) xE5X+2 d) y = In (2x) Y₁ = Y y' =

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Q: Which of the following gives the length of the curve y x2 + 2x from x = 0 to x = 5 ? (x2 + 2x) dæ I…

A: Length of the given curve will be

Q: x(t) y(t) = 3 sin t 8 cos t 0<t< 2n a) What does the curve described by these parametric equations…

A: Recall: Equation of line: y-y1=mx-x1 ; where m=dydx or  y2-y1x2-x1 Length of the curve…

Q: Let C be the curve given by X- Sin/tr) and y=t, from ĭst 55. sin/tT and y=t, from ist E5. Find the…

A: According to Fundamental Theorem of Line Integral, the definite integral of a function is evaluated…

Q: Calculate the line integral [F•dr, where F = 3x°yi + x'j in two cases for C1 and C2. These two…

A: The given vector is F=3x2yi+x3j Here we use Green's theorem. So the Green's theorem is…

Q: Find the slope of the tangent to the curvey=cos²x-sin'x at x- O a) 1 O b) 1/1/2 Oc) -2 d) 2

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Q: 6a) Let A be the parabolic arc defined by the equation y = 8x – x´ over the domain interval [0, 8].…

A: (a) Consider the given function. y=8x-x2 Now, draw the above function by using the calculator.

Q: sin(2t), y = – cos(2t), z = 4t at P(0, 1, 27) has equation 87 + 2 sin(1). The normal plane to the…

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Q: (z)dz

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Q: Find the slope of the tangent line to the parametric curve 2te x(t) y(t) at the point P(0, 1). 2t +e…

A: xt=2t etyt=2t+etAt  P 0,1,  x=0,   y=1  ∴x=0⇒2t et=0             ⇒t=0   dxdt=ddt2t et= 2 t…

Q: For the curve r-y +2xy-y+1=0: a) Find the derivative dy/dx. b) Where do the horizontal tangent lines…

A: follow the next step

Q: Find the domain of the vector function 7(t) = Domain: {t| <t< }

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Q: (x² + y?)3/2' + (x² + y?)3/2J OVer the curve F(t) = (e' cos(t))i+ (e' sin(t))j from the point (1,0)…

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Q: 2- Find the equation of the tangents to curve given parametrically by Y= sin(x²) + 1 at (x,y)= (…

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Q: 1. The parametric equations for the astroid below are x = sin' (t), y =- cos (1) on 0<t < 2a. a)…

A: Given, the parametric equation for the astroid below are  First need to find the stating point on…

Q: Does f(z)=z/(sin z)^2 have a pole of order 1 or 2 at z=0?

A: f(z)=zsin2zFor the poles first we look at the zeros of the denominatorat z=0 We know sin(z) has a…