MathDB

Consider a parameterized curve

C: x=e^{-t}\cos t,\ y=e^{-t}\sin t\left (0\leq t\leq \frac{\pi}{2}\right).

(1) Find the length

L

C

.
(2) Find the area

S

of the region enclosed by the

x,\ y

axis and

C

.
Please solve the problem without using the formula of area for polar coordinate for Japanese High School Students who don't study it in High School.
1997 Kyoto University entrance exam/Science

Problem Statement