Find an integral for the area of the surface generated by revolving the parametric curve about the x-axis: x = sin?t y = sin(2t) osts TT 2 2 T 2 sin(2t)v (cos²t)² + (2cos(2t))? dt sin(2t)/ (2cost)²+(2cos(2t))² dt |? sin(2t)v/ (2sintcost)? + (2cos(2t))? dt O 2n (7 sin?t/(2sintcost)? + (2cos(2t))? dt TT |E sin?t/(2cost)?+(2cos(2t))? dt |2 sin?ty (cos?t) + (2cos(2t))? dt None of these

Q: dy ecos (2t). Find an expression for -for Consider the parametric curve x (t) = -esin (3t) and y (t)…

A:

Q: a) Evaluate Vx² + y² dydx. 1 J-Vi b) Evaluate the line integral | cos x cos y da + (1 – sin æ sin y)…

A:

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 the area of the surface obtained by rotating the curve of parametric equations x = 10 cos³ 10…

A:

Q: Find the area of the surface obtained by rotating the curve x = 6 cos 0, y = 6 sin³ 0, 0< 0 <n/2 %3D…

A:

Q: x = 7 te', y = (t + 1)e', 0stsi Set up an integral that represents the area of the surface obtained…

A:

Q: Consider the parametric curve 5 + cost y = 1+ sint. x=

A:

Q: Find dy/dx and d^2y/dx^2.

A: Given

Q: III. Find the parametric equations of normal line to the surface given by f(x, y) = tan 2 V + y? at…

A:

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: Find dy/dx and d²y/dx² at t = 2 for the parametric curve x = ½t², y = ⅓t ³.

A:

Q: (ii) Find for the parametric equations dx2 dy x =t – sint, y = 1 – cost

A:

Q: - 1. Evaluate the x for parametric equations x = 3t² – 6t a y = 3t³ + 3t with respect to the…

A:

Q: dy for the parametric curve x= 2e', y= sin(1 + e' ) dx Find

A:

Q: Find an equation of the tangent plane to the parametric surface Ř(u, v) = : ((u — sin u) cos v, (1 −…

A:

Q: Use one of the formulas in (5) to find the area under one arch of the cycloid x = t - sint and y =…

A: