Math $1$B HW#$13$ Additional Material Calculus in Polar Coordinates and Parametric Coordinates

Consider the curve $x(t)=e^t-t$ and $y(t)=4e^{\frac{t}{2}}$ for $-8t3.$ Graph the curve and

find its length. Show all work.

Consider the curve $r=2cos3$ shown below.

A$.$ Find the area the curve encloses. Show all work.

B$.$ Set up a definite integral that will give the length of the curve. Show all work.

C$.$ Approximate the length of the curve using Trapezoids with $4$ subdivisions. Show all

work.