MathDB

Let

C

be the parameterized curve for a given positive number

r

and

0\leq t\leq \pi

, C: \left\{\begin{array}{ll} x \equal{} 2r(t \minus{} \sin t\cos t) & \\ y \equal{} 2r\sin ^ 2 t & \end{array} \right. When the point

P

moves on the curve

C

, (1) Find the magnitude of acceleralation of the point

P

at time

t

. (2) Find the length of the locus by which the point

P

sweeps for

0\leq t\leq \pi

. (3) Find the volume of the solid by rotation of the region bounded by the curve

C

and the

x

-axis about the

x

-axis. Edited.

Problem Statement