Barrons AP Calculus

40.

41.

42.

(A)     Total   distance    is  

(A)  Arc     length  is  given   by  dx.     Here    the     integrand  

implies that        hence,  y = 3   ln  x + C.  Since   the curve   contains    (1,2),

2   =   3   ln  1   + C,    which   yields  C   =   2.

(C) The velocity    functions   are

v 1     =   −2t sin (t^2    +   1)  and 

When    these   functions   are graphed on  a   calculator, it  is  clear   that    they

intersect   four    times   during  the first   3   sec,    as  shown   below.

Section II Free-Response