_____________________________________________________________________
Calculus II Quiz
#1 February
14, 2005
Name____________________ R. Hammack Score
______
_____________________________________________________________________
(1) Find
the following antiderivatives.
(a) ∫(2++x+1)dx
= +ln|x|++x+C
(b) ∫(
-(x))dx
=
-tan(x)+C
(c) ∫sec(4x)tan(4x)
dx
= ∫sec(4x)tan(4x)
4dx
= ∫sec(u)tan(u)
4du= sec(u)+C=sec(4x)+C
u = 4x
du = 4dx
(d) ∫dx= ∫cos(x)dx=∫du=ln|u|+C=ln|5+sin(x)|+C
u = 5+sin(x)
du = cos(x)dx
(2) Find the
exact value of the following sums.
(a) (2+)= (2)+()=
(100·2)+(-+-+-+
...-+
)
= 200 + 0 = 200
(b) cos(2k
π)= cos(2 π)+cos(4 π)+cos(6 π)+...+cos(200 π)=1+1+1+...+1
= 100