Problem 6
The coordinates of points on a parametric curve are given by the following parametric equations,
x = $e^t \cos t$
y = $e^t \sin t$
for 0 ? t ? ?.
Use these parametric equations to answer the questions in parts 1 and 2.
Problem 6 - Part 1
(Fill in the Blank): Find the arc length of the parametric curve for 0 ? t ? ?.
For full credit, please show the integral, the method used to evaluate the integral, and other relevant calculations.
L = <your answer here>
Problem 6 - Part 2
(Fill in the Blank): Find the surface area of the parametric curve revolved around the x-axis for 0 ? t ? ?.
For full credit, please show the integral, the method used to evaluate the integral, and other relevant calculations.
S = <your answer here>
