Question

Consider the parametric curve given by
x(t) = 16 sin3(t), y(t) = 13 cos(t) − 5 cos(2t) − 2 cos(3t) − cos(4t),

where t denotes an angle between 0 and 2π.

(a) Sketch a graph of this parametric curve.
(b) Write an integral representing the arc length of this curve.

(c) Using Riemann sums and n = 8, estimate the arc length of this curve.
(d) Write an expression for the exact area of the region enclosed by this curve.

Answer 1

`Hey,

Note: Brother in case of any queries, just comment in box I would be very happy to assist all your queries

Parametric curve is

2)

dy/dt=10*sin(2*t) + 6*sin(3*t) + 4*sin(4*t) - 13*sin(t)

dx/dt=48*cos(3*t)

dy/dx=(10*sin(2*t) + 6*sin(3*t) + 4*sin(4*t) - 13*sin(t))/(48*cos(3*t))

dx=48*cos(3*t)dt

So, arc length is

So, arc length is 4.2421

Note: Brother according to HOMEWORKLIB RULES we are only allowed to answer first 2 part if there are many. So, I request you to post other part as separate posts.

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