Evaluate the line integral. 5)ſ y³ dx + x² dy, C is the arc of the parabola x = 1 - y² from (0,-1) to (0,1)

Q: Find a function y = f(x) that describes the parametric x = -2t + 1, y = 3t², for – o <t < ∞. curve

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Q: Use Green's Theorem to compute y dx+(x³+3xy²) dy where C is the closed curve around the triangle…

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Q: Find the antiderivative of the functions. S 6x dx S(12x - 5)dx S 3dx S(2x2 + 3)dx 1.) 2.) 3.) 4.)…

A: 1. ∫6x dx2. ∫12x-5dx3. ∫3 dx

Q: c) A curve has a parametric equation x = 2t - 1 and y = t* -t'. dy Evaluate dx? 1 at t = 2

A: Given, The parametric equations x=2t3-1, y =t4-t3.

Q: At which point does the parametric curve given by x = 2 cost y = 2 sin t z = 2t - π/3 cross the…

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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: dx Xex+10, Complete the Square.

A: Given,          ∫1x2+6x+10dx

Q: Q.2 Differentiate the function y = 2x - 3x + 4 2) y = xcosx 3) y (1 + x2)3 sinx 4) y = 5) y = tan x…

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Q: Find the tangent plane to the equation z = 6y cos(4x – 2y) at the point (2,4,24) Z =

A: It is given that z=6ycos4x-2y and the point is 2,4,24. Recall the fact that if the equation of the…

Q: Find the curve y if dy = x2 +5, dx + 5, curve passes through (0, 25)***

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Q: 4. Find the parametric equation of the tangent line to r(t) = 4costi – 3tj %3D at Po(2, –n)

A: Given: To find the parametric equation of the given tangent line as follows, r(t) = 4 costi- 3tj…

Q: Find the length of the curve ƒ1x2= x3&gt;2 between x = 0 and x = 4 (as shown).

A: Given curve is fx=x32. To find the length of curve between x=0 and x=4. Solution: We know that…