Problems

Consider the following parametric curve:

$x=t^2-4$

$y=t^2-2t2$

a$.[3$ pts$]$ Carefully graph the curve from $t=-3$ to $t=3.($Feel free to use a computer graphing system for this!$)$ Mark and label the points on this curve corresponding to Integer values of $t.$

b$.[4$ pts$]$ There are two sections of this curve that span $-4x0.$ Set up an integral that expresses the area between the upper of those two sections and the $x-$axis. Then evaluate the integral.

c$.[3$ pts$]$ Set up and simplify the integral that represents the length of the curve from the point $(-4,2)$ to the point $(5,5).$ Then use a computer algebra system to evaluate it$.$