Could you help me with number 2 Ws18. Group_1) Given F(x, y, z) = x³ i + 3yj - z4 k and the curve Cparametrized by r(t) = (sint, cost,t), t = [0, π] evaluateF.idx and F. k dza)b) F.T dsc) Consider the closed curve C' obtained by the union of C and thesegment that joins the points (0,-1, π) and (0,1,0). Evaluate theintegral of F along C' and verify that it is equal to zero.2) a) Show that any vector field in the form of F(x, y, z) = f(x)i +g(y)j + h(z) k where f, g and h are continuous functions thatdepend only on one variable, is a gradient field.b) Evaluate the integral of the vector field F(x,y,z)= sinxi +In(y^2 + 1)j over the "crazy curve" parametrized byr(t) = t(t-1) et³ +4 sint/(1+ cos² (4t - 7)) i + t(t² —1) (tan t³ + 4 sin t)/(1+ e4t-7) j, t = [0,1]

Gradient vector field F if and only if curl of F is zero.

Answered: 2) a) Show that any vector field in the…

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.6: Parametric Equations

Problem 5ECP: Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle...

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