1. (12 points) Consider the loop formed by the parametric curve r(t) = 3t-t, y(t) =...

Transcribed Image Text:

1. (12 points) Consider the loop formed by the parametric curve r(t) = 3t-t³, y(t) = 31², -∞ < 1<∞. -10 10 (a) (6 points) Compute the area of the region enclosed by the loop, i.e., the shaded region in the graph above. (b) (6 points) Compute the length of the segment of the curve that forms the loop. 1. (12 points) Consider the loop formed by the parametric curve r(t) = 3t-t³, y(t) = 31², -∞ < 1<∞. -10 10 (a) (6 points) Compute the area of the region enclosed by the loop, i.e., the shaded region in the graph above. (b) (6 points) Compute the length of the segment of the curve that forms the loop.